Journal articles: 'Switched linear/nonlinear systems'

1

Otanez, Paul G., and Mark E. Campbell. "Bounded Switched Linear Estimator for Smooth Nonlinear Systems." IEEE Transactions on Control Systems Technology 15, no. 2 (March 2007): 358–68. http://dx.doi.org/10.1109/tcst.2006.886436.

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Farshidian, Farbod, Maryam Kamgarpour, Diego Pardo, and Jonas Buchli. "Sequential Linear Quadratic Optimal Control for Nonlinear Switched Systems." IFAC-PapersOnLine 50, no. 1 (July 2017): 1463–69. http://dx.doi.org/10.1016/j.ifacol.2017.08.291.

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3

Dong, Xiaoxiao, Linyan Chang, Fangfang Wu, and Na Hu. "Tracking Control for Switched Cascade Nonlinear Systems." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/105646.

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The issue ofH∞output tracking for switched cascade nonlinear systems is discussed in this paper, where not all the linear parts of subsystems are stabilizable. The conditions of the solvability for the issue are given by virtue of the structural characteristics of the systems and the average dwell time method, in which the total activation time for stabilizable subsystems is longer than that for the unstabilizable subsystems. At last, a simulation example is used to demonstrate the validity and advantages of the proposed approach.

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4

Xu, Hui, and Min Wang. "Robust H1 control for a class of switched nonlinear systems." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 2 (April 15, 2016): 5870–79. http://dx.doi.org/10.24297/jam.v12i2.537.

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This article is concerned with the robust H1 control problem of a class of switched nonlinear systems with norm-bounded time-varying uncertainties. The system considered in this class is composed of two parts: a uncertain linear switched part and a nonlinear part, which is also switched systems. Under the circumstances, that the H1 control problem of all subsystems are not all solvable, the switched feedback control law and the switching law are designed using the average dwell-time method. The corresponding closed-loop switched system is exponentially stable and achieves a weighted L2-gain.

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5

Zong, Xiao Ping, Miao Zhang, and Pei Guang Wang. "Adaptive Controller Design for SISO Switched Nonlinear Systems with Linear Uncertain Parameters." Applied Mechanics and Materials 602-605 (August 2014): 1362–66. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.1362.

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This paper presents that single input single output (SISO) switched nonlinear system tracks the variation of the state error to approach the excepted values by using model reference adaptive control (MRAC) method. In order to improve the adaptive control for nonlinear systems by Using Narendra method and dividing the system into two parts: linear and nonlinear parts. The controllers are designed to guarantee that the systems are closed to the model reference system with the arbitrary switching signal. Switching systems can ensure choose the best controller so that can enhance the performance. The adaptive laws are given that are based on a class of feedback single input single output nonlinear uncertain systems which can switch feedback linear standard models. The adaptive laws are different from the classic adaptive laws, because they vary with different switching signals until the best matching one comes. Simulation results show that the proposed method is effective.

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Wu, Cai Yun, and Ben Niu. "Robust Stabilization for a Class of Switched Nonlinear Systems." Advanced Materials Research 490-495 (March 2012): 1536–40. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1536.

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This paper addresses the stabilization problem for a class of switched nonlinear systems with Lipschitz nonlinearities using the multiple Lyapunov functions (MLFs) approach. A state feedback controller and a state dependent switching law are proposed to asymptotic stabilization the switched system via linear matrix inequalities (LMI). The developed control strategy ensures asymptotic stability of the closed-loop system even if the nonlinear part . Finally, the feasibility of the proposed method is illustrated through a simulation example

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Zhang, Xia, Zun-Quan Xia, and Yan Gao. "Exponential Stabilizability of Switched Systems with Polytopic Uncertainties." Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/853170.

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The exponential stabilizability of switched nonlinear systems with polytopic uncertainties is explored by employing the methods of nonsmooth analysis and the minimum quadratic Lyapunov function. The switchings among subsystems are dependent on the directional derivative along the vertex directions of subsystems. In particular, a sufficient condition for exponential stabilizability of the switched nonlinear systems is established considering the sliding modes and the directional derivatives along sliding modes. Furthermore, the matrix conditions of exponential stabilizability are derived for the case of switched linear system and the numerical example is given to show the validity of the synthesis results.

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8

Zhao, Jianrong, and Wei Liu. "Sampled-data control for switched neutral systems with quantization input under asynchronous switching." Transactions of the Institute of Measurement and Control 40, no. 16 (January 25, 2018): 4287–97. http://dx.doi.org/10.1177/0142331217745353.

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This paper is concerned with sampled-data control for switched neutral systems with quantization input under asynchronous switching. By combining the multiple function method and the average dwell time technique, a lemma gives input-to-state stability conditions for switched nonlinear neutral systems. Considering the relationship between the sampling periods and minimal dwell time of two switching instants, sampled-data control is extended into the input-to-state stability of switched neutral systems under asynchronous switching. The sector bound approach is used to analyse quantization phenomena. For switched linear neutral systems with nonlinear perturbations and quantization input, linear matrix inequality conditions are given to guarantee input-to-state stability. Then, a sampled-data based controller with transmission delays is designed. In the end, the effectiveness of the results is illustrated by a simulation example about the management of forests.

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Kermani, Marwen, and Anis Sakly. "On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays." Mathematical Problems in Engineering 2018 (August 16, 2018): 1–14. http://dx.doi.org/10.1155/2018/6354979.

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This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.

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10

Yang, Junqi, Yantao Chen, Zheng Zheng, and Wei Qian. "Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs." Transactions of the Institute of Measurement and Control 40, no. 4 (October 31, 2016): 1082–91. http://dx.doi.org/10.1177/0142331216673697.

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This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

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11

Liu, Xiu, Shou Ming Zhong, and Xiu Yong Ding. "Exponential Stability for Uncertain Switched Neutral Systems with Nonlinear Perturbations." Advanced Materials Research 217-218 (March 2011): 668–73. http://dx.doi.org/10.4028/www.scientific.net/amr.217-218.668.

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The global exponential stability for switched neutral systems with time-varying delays and nonlinear perturbations is investigated in this paper. LMI-based delay-dependent criterion is proposed to guarantee exponential stability for our considered systems under any switched signal. Lyapunov-Krasovskii functional and Leibniz-Newton formula are applied to find the stability results. Free weighting matrix and linear matrix inequality (LMI) approaches are used to solve the proposed conditions.

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12

Lin, Xiangze, Xueling Li, Yun Zou, and Shihua Li. "Finite-time stabilization of switched linear systems with nonlinear saturating actuators." Journal of the Franklin Institute 351, no. 3 (March 2014): 1464–82. http://dx.doi.org/10.1016/j.jfranklin.2013.11.013.

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13

Huang, Z. H., Y. V. Venkatesh, C. Xiang, and T. H. Lee. "Frequency-domainL2-stability conditions for switched linear and nonlinear SISO systems." International Journal of Systems Science 45, no. 3 (September 20, 2012): 682–701. http://dx.doi.org/10.1080/00207721.2012.724199.

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14

Su, Qingyu, Xiaolong Jia, and Zhengfan Song. "Fault Detection for Discrete-Time Nonlinear Impulsive Switched Systems." Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/694319.

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This paper investigates the fault detection problem for discrete-time nonlinear impulsive switched systems. Attention is focused on designing the fault detection filters to guarantee the robust performance and the detection performance. Based on these performances, sufficient conditions for the existence of filters are given in the framework of linear matrix inequality; furthermore, the filter gains are characterized by a convex optimization problem. The presented technique is validated by an example. Simulation results indicate that the proposed method can effectively detect the faults.

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15

SAITO, TOSHIMICHI, TAKAHIRO KABE, YUKI ISHIKAWA, YUSUKE MATSUOKA, and HIROYUKI TORIKAI. "PIECEWISE CONSTANT SWITCHED DYNAMICAL SYSTEMS IN POWER ELECTRONICS." International Journal of Bifurcation and Chaos 17, no. 10 (October 2007): 3373–86. http://dx.doi.org/10.1142/s021812740701910x.

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This paper overviews nonlinear dynamics of switching power converters which are common objects in dynamical system theory and power electronics. First, complex dynamics of single switching power converters is discussed. Their nonlinear switching can cause rich chaotic and bifurcation phenomena including complicated superstable periodic behavior in discontinuous conduction mode. Second, paralleled converters with winner-take-all switching is discussed. This system can realize multiphase synchronization relating to current sharing with smaller ripple for low-voltage high-current capabilities. Analysis of the dynamics is performed through simple models having piecewise constant vector field and piecewise linear trajectories. Third, simple hardware implementation method is shown and typical phenomena are confirmed experimentally. Finally some future problems are discussed.

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16

Guo, Jian, Chao Liu, and Zhengrong Xiang. "Robust Finite-TimeH∞Control for Impulsive Switched Nonlinear Systems with State Delay." Mathematical Problems in Engineering 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/830154.

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This paper investigates robust finite-timeH∞control for a class of impulsive switched nonlinear systems with time-delay. Firstly, using piecewise Lyapunov function, sufficient conditions ensuring finite-time boundedness of the impulsive switched system are derived. Then, finite-timeH∞performance analysis for impulsive switched systems is developed, and a robust finite-timeH∞state feedback controller is proposed to guarantee that the resulting closed-loop system is finite-time bounded withH∞disturbance attenuation. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.

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17

Xiang, Chang Cheng, Xiu Liu, and Xiu Yong Ding. "Robust Stability of Uncertain Switched Delay Systems with Nonlinear Perturbations." Advanced Materials Research 228-229 (April 2011): 782–88. http://dx.doi.org/10.4028/www.scientific.net/amr.228-229.782.

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This paper focuses on the stability problem of a class of uncertain switched delay systems with nonlinear perturbations. Applying multiple functional technique, we establish a delay dependent stability condition via designing appropriate switching rule. It should emphasize that this result is a standard extension of linear delay differential equations. Meanwhile, this result is presented by LMIs and thus solved easily.

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18

ZHAO, SHOUWEI, and JITAO SUN. "A LIE ALGEBRAIC CONDITION OF STABILITY FOR HYBRID SYSTEMS AND APPLICATION TO HYBRID SYNCHRONIZATION." International Journal of Bifurcation and Chaos 19, no. 01 (January 2009): 379–86. http://dx.doi.org/10.1142/s0218127409022932.

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In this paper, we first present a Lie algebraic condition for global exponential stability of linear switched and impulsive systems. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Hurwitz/Schur stable we derive a new criterion for global exponential stability of linear switched and impulsive systems. Then a simple sufficient condition in terms of Lie algebra is established for a nonlinear system synchronization using a hybrid switched and impulsive control. As an application, Chua's chaotic circuit's synchronization is investigated by our method while synchronization cannot be achieved with the existing result.

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19

Shi, Shuhui, Guoliang Wang, Jianhua Wang, and Hong Li. "Passive Control of Switched Singular Systems via Output Feedback." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/573950.

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An instrumental matrix approach to design output feedback passive controller for switched singular systems is proposed in this paper. The nonlinear inequality condition including Lyapunov inverse matrix and controller gain matrix is decoupled by introducing additional instrumental matrix variable. Combined with multiple Lyapunov function method, the nonlinear inequality is transformed into linear matrix inequality (LMI). An LMI condition is presented for switched singular system to be stable and passive via static output feedback under designed switching signal. Moreover, the conditions proposed do not require the decomposition of Lyapunov matrix and its inverse matrix or fixing to a special structure. The theoretical results are verified by means of an example. The method introduced in the paper can be effectively extended to a single singular system and normal switched system.

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20

Bortakovsky, A. S., and I. V. Uryupin. "COMPUTER TECHNOLOGY OF SYNTHESIS OPTIMAL LINEAR SWITCHED SYSTEMS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 185 (November 2019): 13–20. http://dx.doi.org/10.14489/vkit.2019.11.pp.013-020.

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The linear-quadratic problem of synthesis optimal control of switched systems is considered. Continuous change of state of the system is described by linear differential equations, and instantaneous discrete changes of state (switching) – linear recurrent equations. The moments of switching, and their number is not prespecified. The quality of control is characterized by a quadratic functional, which takes into account the cost of each switch. The considered problem generalizes the classical linear-quadratic problems of optimal control of continuous, discrete and continuous-discrete systems, transferring them to a new class of dynamic systems – switchable (hybrid) control systems. Together with the problem of optimal control synthesis, the problem of minimizing the number of switchings, characteristic of hybrid systems, is relevant. The peculiarity of the synthesis of optimal switchable systems is that the price function in the considered problem is not quadratic. Therefore, it is proposed to build a price function from auxiliary, so-called price moment functions, each of which is defined as the minimum value of the quality functional at fixed switching moments and is quadratic. At the same time, the optimal positional control, linear in state, depends nonlinearly on switching moments. Optimization of these moments becomes the last stage of the synthesis. The proposed computer-aided synthesis technology makes it possible to find the optimal “controlling complex”, including the number of switches, the switching moments, as well as the control of continuous and discrete movements of the system. The application of the developed technology is demonstrated on an academic example of synthesis.

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Wei, Jincheng, Peng Shi, Hamid Reza Karimi, and Bo Wang. "BIBO Stability Analysis for Delay Switched Systems with Nonlinear Perturbation." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/738653.

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The problem of bounded-input bounded-output (BIBO) stability is investigated for a class of delay switched systems with mixed time-varying discrete and constant neutral delays and nonlinear perturbation. Based on the Lyapunov-Krasovskii functional theory, new BIBO stabilization criteria are established in terms of delay-dependent linear matrix inequalities. The numerical simulation is carried out to demonstrate the effectiveness of the results obtained in the paper.

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22

Xu, Peng, Fei Long, Qixiang Wang, Ji Tian, Xiaowu Yang, and Lipo Mo. "Finite-Time Stability for Caputo Nabla Fractional-Order Switched Linear Systems." Fractal and Fractional 6, no. 11 (October 25, 2022): 621. http://dx.doi.org/10.3390/fractalfract6110621.

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In this paper, we address the finite-time stability problem of Caputo nabla fractional-order switched linear systems with α∈(0,1). Firstly, the monotonicity of the discrete Mittag-Leffler function is proposed. Secondly, under the per-designed switching rules, the form of the solution for Caputo nabla fractional-order switched linear systems is obtained by using the discrete unit step function. On the above basis, some sufficient conditions of finite-time stability for Caputo nabla fractional-order switched linear systems are proposed, according to the discrete Grönwall inequality and the monotonicity of the discrete Mittag-Leffler function. Finally, simulation verification is carried out via three numerical examples.

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23

Alwan, Mohamad S., and Xinzhi Liu. "On stability of linear and weakly nonlinear switched systems with time delay." Mathematical and Computer Modelling 48, no. 7-8 (October 2008): 1150–57. http://dx.doi.org/10.1016/j.mcm.2007.12.024.

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Li, Ping, and Shou-Ming Zhong. "BIBO stabilization of piecewise switched linear systems with delays and nonlinear perturbations." Applied Mathematics and Computation 213, no. 2 (July 2009): 405–10. http://dx.doi.org/10.1016/j.amc.2009.03.029.

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25

Zhang, Shitao, Peng Lin, and Junfeng Zhang. "Event-Triggered Asynchronous Filter of Nonlinear Switched Positive Systems with Output Quantization." Mathematics 10, no. 4 (February 15, 2022): 599. http://dx.doi.org/10.3390/math10040599.

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This paper deals with a static/dynamic event-triggered asynchronous filter of nonlinear switched positive systems with output quantization. The nonlinear function is located in a sector. Both static and dynamic event-triggering conditions are established based on the 1-norm form. By virtue of the event-triggering mechanism, the error system is transformed into an interval uncertain system. An event-triggered asynchronous filter is designed by employing a matrix decomposition approach. The positivity and L1-gain stability of the error system are guaranteed by means of linear copositive Lyapunov functions and a linear programming approach. Finally, two examples are given to verify the effectiveness of the design.

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26

Liu, Leipo, Xiangyang Cao, Bo Fan, and Zhumu Fu. "L1 Input-Output Finite-Time Control of Positive Switched Nonlinear Systems." Mathematical Problems in Engineering 2019 (August 7, 2019): 1–10. http://dx.doi.org/10.1155/2019/9132906.

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In this paper, the problem of L1 input-output finite-time control of positive switched nonlinear systems with time-varying and distributed delays is investigated. Nonlinear functions considered in this paper are located in a sector field. Firstly, the proof of the positivity of switched positive nonlinear systems with time-varying and distributed delays is given, and the concept of L1 input-output finite-time stability (L1 IO-FTS) is firstly introduced. Then, by constructing multiple co-positive-type nonlinear Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are derived to guarantee the corresponding closed-loop system is L1 IO-FTS. Such conditions can be easily solved by linear programming. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

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27

Hariprasad, K., Sharad Bhartiya, and Ravindra D. Gudi. "A multiple linear modeling approach for nonlinear switched systems1." IFAC Proceedings Volumes 45, no. 15 (2012): 63–68. http://dx.doi.org/10.3182/20120710-4-sg-2026.00030.

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28

Abou Al-Ola, Omar M., Ken'ichi Fujimoto, and Tetsuya Yoshinaga. "Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System." Mathematical Problems in Engineering 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/723509.

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Many problems with control theory have led to investigations into switched systems. One of the most urgent problems related to the analysis of the dynamics of switched systems is the stability problem. The stability of a switched system can be ensured by a common Lyapunov function for all switching modes under an arbitrary switching law. Finding a common Lyapunov function is still an interesting and challenging problem. The purpose of the present paper is to prove the stability of equilibrium in a certain class of nonlinear switched systems by introducing a common Lyapunov function; the Lyapunov function is based on generalized Kullback–Leibler divergence or Csiszár'sI-divergence between the state and equilibrium. The switched system is useful for finding positive solutions to linear algebraic equations, which minimize theI-divergence measure under arbitrary switching. One application of the stability of a given switched system is in developing a new approach to reconstructing tomographic images, but nonetheless, the presented results can be used in numerous other areas.

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29

Souza, Wallysonn Alves de, Marcelo Carvalho Minhoto Teixeira, Máira Peres Alves Santim, Rodrigo Cardim, and Edvaldo Assunção. "Robust Switched Control Design for Nonlinear Systems Using Fuzzy Models." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/721537.

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The paper proposes a new switched control design method for some classes of uncertain nonlinear plants described by Takagi-Sugeno fuzzy models. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology eliminates the need to find the membership function expressions to implement the control laws. The control designs of a ball-and-beam system and of a magnetic levitator illustrate the procedure.

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30

Wang, Na, and Lai Jun Lu. "The Fault Diagnosis of a Class of Time-Delay Switched Systems." Advanced Materials Research 960-961 (June 2014): 774–79. http://dx.doi.org/10.4028/www.scientific.net/amr.960-961.774.

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The actual engineering control systems are nonlinear [1-2] and uncertainty [3-4] at the same time, so the robustness and fault diagnosis of systems are more meaningful [5-6]. Sometimes the system is with switching characteristics, which makes the study of switched systems more meaningful. As one of the nonlinear systems, switched systems exist in the practical systems widely, and the phenomenon of delay exists in industrial control nature, or in the life of people widely [7-8]. So the fault diagnosis research [11-12] of nonlinear switched systems with time-delay [9-10] has attracted the attention of many scholars. Motivated with the above issues, the general form of a class of switched systems with time-delay is described in detail, which also mentioned lemma 1 (Schur complement lemma) and lemma 2, the two lemmas will be applied to the proof process of the conclusion. The core part is observer design for time-delay systems fault, which puts forward the uniformly bounded stable condition of fault estimation error system expressed as the linear matrix inequality, and Lyapunov stability is applied to the strict proof. At last, the simulation of MATLAB in a numerical example proved the validity of the conclusion.

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Wang, Yongzhao. "Exponential Stabilization for a Class of Nonlinear Switched Systems with Mixed Delays under Asynchronous Switching." Complexity 2018 (August 30, 2018): 1–11. http://dx.doi.org/10.1155/2018/7692375.

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This paper deals with the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching. The switching signal of the switched controller involves delay, which results in the asynchronous switching between the candidate controllers and subsystems. By constructing the parameter-dependent Lyapunov-Krasovskii functional and the average dwell time approach, some sufficient conditions in forms of linear matrix inequalities are presented to ensure the exponential stability of the switched nonlinear system under arbitrary switching signals. In addition, through the special deformation of the matrix and Schur complement, the controllers with asynchronous switching are designed. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results.

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Horváth, Zsolt, and András Edelmayer. "An Algorithm for the Calculation of the Dwell Time Constraint for Switched ℋ∞ Filters." Acta Universitatis Sapientiae Electrical and Mechanical Engineering 10, no. 1 (December 1, 2018): 5–19. http://dx.doi.org/10.2478/auseme-2018-0001.

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Abstract This paper presents a numerical algorithm for determining the minimum dwell time constraint for switched linear ℋ∞ fault detection filters. When applying switched systems, ensuring the stability is a crucial target, which can be guaranteed, when we switch slowly enough between the subsystems, more precisely when the intervals between two consecutive switching instants, called dwell time, are large enough. The problem formulation is based on multiple Lyapunov functions and is expressed through a special form of linear matrix inequalities (LMIs), which include a nonlinear term of the dwell time. This represents a multivariable, time dependent optimization problem. As a result, the task cannot be treated as a simple feasibility problem involving a LMI solver as it is widely used in applications of the linear control. To solve these special LMIs, we propose a numerical algorithm, called 𝒯d-iteration, which combines the procedure of interval halving with an LMI solver. The algorithm implemented in MATLAB shows its applicability as well as suggest further benefits for the switched linear control and filter synthesis.

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Carter, Camille, Jacob Murri, David Reber, and Benjamin Webb. "A simple stability criterion for dynamical systems with stochastic switching and/or stochastic time-delays." Nonlinearity 35, no. 12 (October 18, 2022): 6042–66. http://dx.doi.org/10.1088/1361-6544/ac9505.

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Abstract In many natural and technological systems the rule that governs the system’s dynamics changes over time. In such switched systems the system’s switching can be a significant source of instability. Here we give a simple sufficient criterium to determine if an i.i.d. stochastically switched system is stable in expectation. This method extends recent results for linear switched systems to nonlinear switched systems. It also extends results known for general switched systems giving improved results for systems with i.i.d. stochastic switching. The paper also considers the effects of time-delays on the stability of switched systems. Such time delays, which are intrinsic to any real-world system, can also have a destabilising effect on the system’s dynamics. Previously, it has been shown that if a dynamical system is intrinsically stable, which is a stronger form of global stability, then it maintains its stability even when time-delays are introduced into the system. Here we extend this notion to stochastically switched systems. We refer to this type of stability as patient stability and give a simple sufficient criterium under which such systems are patiently stable, i.e. cannot be destabilised by time delays. Both criteria introduced in this paper side step the need to use Lyapunov, linear matrix inequalities, and semi-definite programming-type methods. Our examples in this paper demonstrate the simplicity of these criteria.

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Li, Zhenhua, Lijun Long, and Jun Zhao. "Linear output-feedback-based semi-global stabilization for switched nonlinear time-delay systems." Journal of the Franklin Institute 356, no. 13 (September 2019): 7224–45. http://dx.doi.org/10.1016/j.jfranklin.2019.06.042.

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Faraji-Niri, Mona, Vahid Asadzadeh, and Javad Rahmani Fard. "Stabilization of Arbitrary Switched Nonlinear Fractional Order Dynamical Systems: Application to Francis Hydro-Turbine Governing System." Information Technology And Control 48, no. 3 (September 24, 2019): 401–14. http://dx.doi.org/10.5755/j01.itc.48.3.20470.

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This paper is a theoretical and practical study on the stabilization of fractional order Lipschitz nonlinear systems under arbitrary switching. The investigated system is a generalization of both switched and fractional order dynamical systems. Firstly, a switched frequency distributed model is introduced as an equivalent for the system. Subsequently, a sufficient condition is obtained for the stabilizability of the system based on the Lyapunov approach. Finally, the results are extended to synthesis mode-dependent state feedback controller for the system. All the results are expressed in terms of coupled linear matrix inequalities, which are solvable by optimization tools and directly reducible to the conditions of the integer order nonlinear switching systems as well as the conventional non-switched nonlinear fractional order systems. The proposed method has various practical implications. As an example, it is utilized to control Francis hydro-turbine governing system. This system is represented as a switching structure and supposed to supply a load suffering abrupt changes driven by an arbitrary switching mechanism. The simulation results support the usefulness of the method.

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Hu, Cheng, Scarlett Chen, and Zhe Wu. "Economic Model Predictive Control of Nonlinear Systems Using Online Learning of Neural Networks." Processes 11, no. 2 (January 20, 2023): 342. http://dx.doi.org/10.3390/pr11020342.

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This work focuses on the development of a Lyapunov-based economic model predictive control (LEMPC) scheme that utilizes recurrent neural networks (RNNs) with an online update to optimize the economic benefits of switched non-linear systems subject to a prescribed switching schedule. We first develop an initial offline-learning RNN using historical operational data, and then update RNNs with real-time data to improve model prediction accuracy. The generalized error bounds for RNNs updated online with independent and identically distributed (i.i.d.) and non-i.i.d. data samples are derived, respectively. Subsequently, by incorporating online updating RNNs within LEMPC, probabilistic closed-loop stability, and economic optimality are achieved simultaneously for switched non-linear systems accounting for the RNN generalized error bound. A chemical process example with scheduled mode transitions is used to demonstrate that the closed-loop economic performance under LEMPC can be improved using an online update of RNNs.

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Zhang, Qi, and Bin Liu. "Switching Stabilization for Nonlinear Networked Control Systems with Delays and Packet Losses." Information Technology And Control 49, no. 2 (June 16, 2020): 302–16. http://dx.doi.org/10.5755/j01.itc.49.2.24612.

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This paper studies the stabilization problem for nonlinear NCSs(NNCSs) with bilateral network-induced random delay and packet dropout. T-S fuzzy model is employed to represent the nonlinear controlled plant. Based on the T-S model, a discrete-time fuzzy switched system model with uncertain parameters is established by means of the uncertain method and switching system method. Furthermore, the exponential stability condition for the state of the fuzzy switched system is obtained by using the combination of slow switching model-dependent average dwell time (MDADT) method and fast switching MDADT method. Finally, a series of rotary inverted pendulum experiments are provided to illustrates the effectiveness of the proposed method and prove that the proposed fuzzy controller based on T-S fuzzy model can balance the rotary inverted pendulum in a greater state range rather than the linear controller based on linearization

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Zhang, Le, and Jinnan Wu. "Reliable Control for Time-Varying Delay Switched Fuzzy Systems with Faulty Actuators Based on Observers Switching Method." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/836749.

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This paper deals with the reliable control problem of nonlinear systems represented by switched fuzzy systems (SFS) with time-varying delay, where each subsystem of switched system is a time-varying delay fuzzy system. A switched fuzzy system with a Takagi and Sugeno (T-S) fuzzy model, which differs from existing ones, is firstly employed to describe a nonlinear system. When the actuators are serious failure, the residual part of actuators cannot make original system stability, using switching technique depends on the states of observers, and the fuzzy reliable controller based on measured observers states instead of the original system states information is built. The stabilization criterion of the reliable control problem is given for the case that the state of original system is unmeasurable. The multi-Lyapunov functions method is utilized to the stability analysis and controller design for time-varying delay switched fuzzy systems with faulty actuators. Moreover, observers switching strategy achieving estimation errors decreasing uniformly asymptotically to zero of the switched fuzzy systems is considered. Finally, the stabilization criterion is transformed into the solvability of sufficient linear matrix inequality (LMI) conditions. To illustrate the effectiveness of the proposed stabilization criterion and controller design approaches, a designed numerical example is studied, and some simulations are provided.

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Jabri, Dalel, Djamel Eddine Chouaib Belkhiat, Kevin Guelton, and Noureddine Manamanni. "Decentralized Controller Design for Large Scale Switched Takagi-Sugeno Systems with H∞ Performance Specifications." Journal of Advanced Engineering and Computation 2, no. 2 (June 30, 2018): 139. http://dx.doi.org/10.25073/jaec.201822.187.

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This paper investigates the design of decentralized controllers for a class of large scale switched nonlinear systems under arbitrary switching laws. A global large scale switched system can be split into a set of smaller interconnected switched Takagi-Sugeno fuzzy subsystems. In this context, to stabilize the overall closed-loop system, a set of switched non-Parallel-Distributed-Compensation (non-PDC) output-feedback controllers is considered. The latter is designed based on Linear Matrix Inequalities (LMI) conditions obtained from a multiple switched non-quadratic Lyapunov-like candidate function. The controllers proposed herein are synthesized to satisfy H∞ performances for disturbance attenuation. Finally, a numerical example is proposed to illustrate the effectiveness of the suggested decentralized switched controller design approach. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wang, Xia, Jun Zhao, and Yujun Tang. "State tracking model reference adaptive control for switched nonlinear systems with linear uncertain parameters." Journal of Control Theory and Applications 10, no. 3 (July 1, 2012): 354–58. http://dx.doi.org/10.1007/s11768-012-1018-6.

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Wasilewski, Maciej, Dominik Pisarski, Robert Konowrocki, and Czesław I. Bajer. "A New Efficient Adaptive Control of Torsional Vibrations Induced by Switched Nonlinear Disturbances." International Journal of Applied Mathematics and Computer Science 29, no. 2 (June 1, 2019): 285–303. http://dx.doi.org/10.2478/amcs-2019-0021.

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Abstract Torsional vibrations induced in drilling systems are detrimental to the condition of the machine and to the effectiveness of the engineering process. The cause of vibrations is a nonlinear and unknown friction between a drill string and the environment, containing jumps in its characteristics. Nonlinear behaviour of the friction coefficient results in self-excited vibration and causes undesirable stick-slip oscillations. The aim of this paper is to present a novel adaptive technique of controlling vibrating systems. The scheme is based on the linear quadratic regulator and uses direct measurements of the friction torque to synthesize its linear dynamic approximation. This approach allows generating a control law that takes into account the impact of the friction on the system dynamics and optimally steers the system to the desired trajectory. The controller’s performance is examined via numerical simulations of the stabilization of the drilling system. The proposed solution outperforms the comparative LQG regulator in terms of the minimization of the assumed cost functional and the overall stability of the control system under the nonlinear disturbance.

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42

Liu, Leipo, Hao Xing, Xiangyang Cao, Zhumu Fu, and Yifan Di. "Asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems." Transactions of the Institute of Measurement and Control 41, no. 14 (June 20, 2019): 4157–66. http://dx.doi.org/10.1177/0142331219841415.

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This paper considers asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems (DNIPSS). Firstly, the definition of input-output finite-time stability (IO-FTS) is introduced. By using the linear co-positive Lyapunov function (LCLF) and average dwell time (ADT) approach, a state feedback controller via asynchronous switching is designed and sufficient conditions are obtained to guarantee the corresponding closed-loop system is IO-FTS. Such conditions can be solved by linear programming. Furthermore, the mode-dependent average dwell time (MDADT) method for asynchronously input-output finite-time control of DNIPSS is also presented. Finally, two examples are provided to show the effectiveness of the proposed method.

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Hernandez–Gonzalez, Miguel, Michael Basin, and Oleg Stepanov. "Discrete-time estimation of switched stochastic polynomial systems and its application to reconstruction of induction motor variables." Transactions of the Institute of Measurement and Control 43, no. 13 (March 24, 2021): 3031–43. http://dx.doi.org/10.1177/0142331221998856.

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This paper presents a solution to the filtering problem for a class of stochastic discrete-time nonlinear polynomial systems with switching in the state equation over linear observations and its application to a mechatronic system. The switching in the state equation is performed between two different nonlinear functions according to a sequence of independent Bernoulli random variables that take the quantities of zero and one. The mean-square filtering solution is obtained for a general nonlinear discrete-time polynomial system and a finite-dimensional system of filtering equations is then obtained for a second degree polynomial system as a particular case. The mean-square estimates of polynomial state terms are expressed as functions of the estimate and covariance matrix. Finally, some numerical simulations are carried out to reconstruct the variable states given a vector output measurement for a linear system, a second degree polynomial system, and an induction motor model to show effectiveness of the proposed algorithm. The proposed method is compared with an extended Kalman filter-based algorithm for discrete-time switched nonlinear systems.

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Xing, Hao, Leipo Liu, Xiangyang Cao, Zhumu Fu, and Shuzhong Song. "Guaranteed cost finite-time control of positive switched nonlinear systems with D-perturbation." Open Mathematics 15, no. 1 (December 29, 2017): 1635–48. http://dx.doi.org/10.1515/math-2017-0141.

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Abstract This paper considers the guaranteed cost finite-time boundedness of positive switched nonlinear systems with D-perturbation and time-varying delay. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the Lyapunov-Krasovskii functional and average dwell time (ADT) approach, an output feedback controller is designed and sufficient conditions are obtained to ensure the corresponding closed-loop systems to be guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, two examples are provided to show the effectiveness of the proposed method.

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Zhang, Ni, Mei Chun Fu, and Tao Zou. "Delay-Dependent Non-Fragile Robust H∞ Control for Switched Systems with Multiple Time Delays." Applied Mechanics and Materials 130-134 (October 2011): 222–26. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.222.

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The non-fragile robust H∞ control problem is investigated for the uncertain switched discrete time systems with multiple state and input time delays. As the system and controller parameters are polytopically uncertain, the delay-dependent sufficient conditions for the existence of the non-fragile robust H∞ controller via state feedback are presented for the systems based on the multiple Lyapunov functions and state dependent switching rules. By using the cone complementarity linearization algorithm, the nonlinear matrix inequalities relevant to the controller design can be transformed into the nonlinear programming problems constrained by the linear matrices. The simulation results show the effectiveness of the controller design method.

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Wang, Yilin, Hamid Reza Karimi, and Zhengrong Xiang. "Delay-Dependent Control for Networked Control Systems with Large Delays." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/643174.

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We consider the problems of robust stability and control for a class of networked control systems with long-time delays. Firstly, a nonlinear discrete time model with mode-dependent time delays is proposed by converting the uncertainty of time delay into the uncertainty of parameter matrices. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of linear matrix inequalities (LMIs). Then, we extend the results to a more practical case where the subsystem occurrence probabilities are uncertain. Finally, a simulation example is presented to show the efficacy of the proposed method.

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Göksu, Gökhan, and Ulviye Başer. "Observer-based H∞ finite-time control for switched linear systems with interval time-delay." Transactions of the Institute of Measurement and Control 41, no. 5 (June 27, 2018): 1348–60. http://dx.doi.org/10.1177/0142331218777559.

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In this work, interval time-delay switched systems having completely unstable and mixed stable matrices of the state vector are considered. An observer-based controller is designed for finite-time boundedness and H∞-control of these systems. New sufficient conditions on the existence of a desired observer are developed and new average dwell-time bounds are introduced separately in case of unstable and mixed stable subsystems. An algorithm is presented for the calculation of unknown constants in the average dwell-time bounds which depend on nonlinear matrices in terms of the cone complementarity linearization method. Finally, numerical examples are given for the effectiveness and validity of the proposed solutions.

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Rajchakit, Grienggrai. "Switching Design for the Asymptotic Stability and Stabilization of Nonlinear Uncertain Stochastic Discrete-time Systems." International Journal of Nonlinear Sciences and Numerical Simulation 14, no. 1 (February 21, 2013): 33–44. http://dx.doi.org/10.1515/ijnsns-2011-0176.

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Abstract This paper is concerned with asymptotic stability and stabilization of nonlinear uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability and stabilization for the nonlinear uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

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Ghalehnoie, Mohsen, Mohammad-Reza Akbarzadeh-Tootoonchi, and Naser Pariz. "Fuzzy control design for nonlinear impulsive switched systems using a nonlinear Takagi-Sugeno fuzzy model." Transactions of the Institute of Measurement and Control 42, no. 9 (January 15, 2020): 1700–1711. http://dx.doi.org/10.1177/0142331219894867.

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This paper deals with the fuzzy control design for nonlinear impulsive switched systems modeled by a novel nonlinear Takagi-Sugeno (T-S) fuzzy structure. To model, this structure only uses some of the nonlinearities as premise variables. So, the derived model has fewer rules compared with the traditional T-S fuzzy models that utilize standard local sector nonlinearity; and accordingly, the number of stability/stabilization conditions is sharply reduced. In our structure, considering only a part of nonlinearities as premise variables causes that some of the local models in the consequent part of the fuzzy rules be nonlinear but with less complexity than the original nonlinear system. As a result, the feasibility of our model’s stability criteria is more than those that one can directly establish for the original nonlinear system. Besides, unlike the existing methods in the literature of impulsive switched systems that aim to permanently reduce the value of Lyapunov function candidates, this paper takes into account this process until trajectories reach a sufficient small region containing the origin. Then, within this region, the size of Lyapunov functions is just controlled at impulse instants. This strategy is useful when there are non-vanishing impulses and/or uncertainties, and it is more relaxed when the goal is ultimate bound stability. Finally, to achieve the stabilizing control signal that ensures practical control issues along with smallest ultimate bound and widest region of attraction, this paper also proposes an optimization problem with linear and bilinear constraints. The simulation results represent the performance of the proposed method.

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Song, Xiaona, Mi Wang, Shuai Song, and Jingtao Man. "Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems." Complexity 2018 (October 17, 2018): 1–11. http://dx.doi.org/10.1155/2018/6215945.

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This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

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Journal articles on the topic 'Switched linear/nonlinear systems'

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