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Journal articles on the topic 'Small-Time stability'

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Published: 8 June 2024

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1

Li, Desheng, and P. E. Kloeden. "Robustness of asymptotic stability to small time delays." Discrete & Continuous Dynamical Systems - A 13, no. 4 (2005): 1007–34. http://dx.doi.org/10.3934/dcds.2005.13.1007.

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2

Khan, Amjad, and Dmitry E. Pelinovsky. "Long-time stability of small FPU solitary waves." Discrete & Continuous Dynamical Systems - A 37, no. 4 (2017): 2065–75. http://dx.doi.org/10.3934/dcds.2017088.

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3

de Gosson, Maurice A., Karlheinz Gröchenig, and José Luis Romero. "Stability of Gabor Frames Under Small Time Hamiltonian Evolutions." Letters in Mathematical Physics 106, no. 6 (May 6, 2016): 799–809. http://dx.doi.org/10.1007/s11005-016-0846-6.

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4

Jia, Hongjie, Xiaodan Yu, Yixin Yu, and Chengshan Wang. "Power system small signal stability region with time delay." International Journal of Electrical Power & Energy Systems 30, no. 1 (January 2008): 16–22. http://dx.doi.org/10.1016/j.ijepes.2007.06.020.

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5

Maller, Ross A., and Peter C. Schmidli. "Small-time almost-sure behaviour of extremal processes." Advances in Applied Probability 49, no. 2 (June 2017): 411–29. http://dx.doi.org/10.1017/apr.2017.7.

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Abstract An rth-order extremal process Δ(r) = (Δ(r)t)t≥0 is a continuous-time analogue of the rth partial maximum sequence of a sequence of independent and identically distributed random variables. Studying maxima in continuous time gives rise to the notion of limiting properties of Δt(r) as t ↓ 0. Here we describe aspects of the small-time behaviour of Δ(r) by characterising its upper and lower classes relative to a nonstochastic nondecreasing function bt > 0 with limt↓bt = 0. We are then able to give an integral criterion for the almost sure relative stability of Δt(r) as t ↓ 0, r = 1, 2, . . ., or, equivalently, as it turns out, for the almost sure relative stability of Δt(1) as t ↓ 0.

6

Grosu, Eran, and Isaac Harari. "Stability of semidiscrete formulations for elastodynamics at small time steps." Finite Elements in Analysis and Design 43, no. 6-7 (April 2007): 533–42. http://dx.doi.org/10.1016/j.finel.2006.12.006.

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7

Tian-guang, Chu, and Wang Zhao-lin. "Technical stability of nonlinear time-varying systems with small parameters." Applied Mathematics and Mechanics 21, no. 11 (November 2000): 1264–71. http://dx.doi.org/10.1007/bf02459247.

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8

Zhu, Jing, Tian Qi, and Jie Chen. "Small-gain stability conditions for linear systems with time-varying delays." Systems & Control Letters 81 (July 2015): 42–48. http://dx.doi.org/10.1016/j.sysconle.2015.04.009.

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9

Giorgilli, Antonio. "Small denominators and exponential stability: From Poincaré to the present time." Rendiconti del Seminario Matematico e Fisico di Milano 68, no. 1 (December 1998): 19–57. http://dx.doi.org/10.1007/bf02925829.

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10

Harari, Isaac. "Stability of semidiscrete formulations for parabolic problems at small time steps." Computer Methods in Applied Mechanics and Engineering 193, no. 15-16 (April 2004): 1491–516. http://dx.doi.org/10.1016/j.cma.2003.12.035.

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11

Ayasun, Saffet. "Computation of time delay margin for power system small-signal stability." European Transactions on Electrical Power 19, no. 7 (October 2009): 949–68. http://dx.doi.org/10.1002/etep.272.

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12

Campomanes, Marc L., and Yusuf Altintas. "An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions." Journal of Manufacturing Science and Engineering 125, no. 3 (July 23, 2003): 416–22. http://dx.doi.org/10.1115/1.1580852.

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This paper presents an improved milling time domain model to simulate vibratory cutting conditions at very small radial widths of cut. The improved kinematics model allows simulation of very small radial immersions. The model can predict forces, surface finish, and chatter stability, accurately accounting for non-linear effects that are difficult to model analytically. The discretized cutter and workpiece kinematics and dynamic models are used to represent the exact trochoidal motion of the cutter, and to investigate the effects of forced vibrations and changing radial immersion due to deflection and vibrations on chatter stability. Three dimensional surface finish profiles are predicted and are compared to measured results. Stability lobes generated from the time domain simulation are also shown for various cases.

13

Karafyllis, I., and J. Tsinias. "Nonuniform in Time Input-to-State Stability and the Small-Gain Theorem." IEEE Transactions on Automatic Control 49, no. 2 (February 2004): 196–216. http://dx.doi.org/10.1109/tac.2003.822861.

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14

Bambusi, Dario. "Long Time Stability of Some Small Amplitude Solutions in Nonlinear Schrödinger Equations." Communications in Mathematical Physics 189, no. 1 (October 1, 1997): 205–26. http://dx.doi.org/10.1007/s002200050196.

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15

Zhu, Jing, and Jie Chen. "Stability of systems with time-varying delays: An ℒ1 small-gain perspective." Automatica 52 (February 2015): 260–65. http://dx.doi.org/10.1016/j.automatica.2014.12.011.

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16

Fukui, Yoshiro. "Stability analysis of homogeneous finite-time PID control using a small gain theorem." IFAC-PapersOnLine 54, no. 14 (2021): 382–87. http://dx.doi.org/10.1016/j.ifacol.2021.10.384.

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17

Johannsson, Hjortur, Arne Hejde Nielsen, and Jacob Ostergaard. "Wide-Area Assessment of Aperiodic Small Signal Rotor Angle Stability in Real-Time." IEEE Transactions on Power Systems 28, no. 4 (November 2013): 4545–57. http://dx.doi.org/10.1109/tpwrs.2013.2271193.

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18

Meinsma, Gjerrit, Minyue Fu, and Tetsuya Iwasaki. "Robustness of the stability of feedback systems with respect to small time delays." Systems & Control Letters 36, no. 2 (February 1999): 131–34. http://dx.doi.org/10.1016/s0167-6911(98)00075-9.

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19

Jianrong Zhang, C. R. Knopse, and P. Tsiotras. "Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions." IEEE Transactions on Automatic Control 46, no. 3 (March 2001): 482–86. http://dx.doi.org/10.1109/9.911428.

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20

Griffin, Philip S., and Ross A. Maller. "Small and large time stability of the time taken for a Lévy process to cross curved boundaries." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 49, no. 1 (February 2013): 208–35. http://dx.doi.org/10.1214/11-aihp449.

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21

Liu, Ming, Fanwei Meng, and Dongpo Hu. "Impacts of Multiple Time Delays on a Gene Regulatory Network Mediated by Small Noncoding RNA." International Journal of Bifurcation and Chaos 30, no. 05 (April 2020): 2050069. http://dx.doi.org/10.1142/s0218127420500698.

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In this paper, the impacts of multiple time delays on a gene regulatory network mediated by small noncoding RNA is studied. By analyzing the associated characteristic equation of the corresponding linearized system, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Furthermore, the explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are given by the center manifold theorem and the normal form theory for functional differential equations. Finally, some numerical simulations are demonstrated for supporting the theoretical results.

22

Xu, Luo, Qinglai Guo, Zhongguan Wang, and Hongbin Sun. "Modeling of Time-Delayed Distributed Cyber-Physical Power Systems for Small-Signal Stability Analysis." IEEE Transactions on Smart Grid 12, no. 4 (July 2021): 3425–37. http://dx.doi.org/10.1109/tsg.2021.3052303.

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23

Morales, Walter, Gabriela Leite, Gonzalo Parodi, Maritza Sanchez, Sarah Ayyad, Stacy Weitsman, Maria Jesus Villanueva-Millan, et al. "Tu1567: THE SMALL BOWEL MICROBIOME DEMONSTRATES STABILITY OVER TIME: DATA FROM THE REIMAGINE STUDY." Gastroenterology 162, no. 7 (May 2022): S—1012—S—1013. http://dx.doi.org/10.1016/s0016-5085(22)62405-3.

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24

Liu, Bo, Wenlian Lu, and Tianping Chen. "Stability analysis of some delay differential inequalities with small time delays and its applications." Neural Networks 33 (September 2012): 1–6. http://dx.doi.org/10.1016/j.neunet.2012.03.009.

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25

Bourles, H. "Local l/sub p/-stability and local small gain theorem for discrete-time systems." IEEE Transactions on Automatic Control 41, no. 6 (June 1996): 903–7. http://dx.doi.org/10.1109/9.506248.

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26

Cong, Nguyen D., Thai S. Doan, and Hoang T. Tuan. "Asymptotic Stability of Linear Fractional Systems with Constant Coefficients and Small Time-Dependent Perturbations." Vietnam Journal of Mathematics 46, no. 3 (February 6, 2018): 665–80. http://dx.doi.org/10.1007/s10013-018-0272-4.

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27

Hsu, M. C., Y. Bazilevs, V. M. Calo, T. E. Tezduyar, and T. J. R. Hughes. "Improving stability of stabilized and multiscale formulations in flow simulations at small time steps." Computer Methods in Applied Mechanics and Engineering 199, no. 13-16 (February 2010): 828–40. http://dx.doi.org/10.1016/j.cma.2009.06.019.

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28

Li, Li. "New Approach to Non-Fragile Control of Uncertain Fuzzy Systems with Time-Delay." Applied Mechanics and Materials 433-435 (October 2013): 1131–35. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.1131.

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This paper focuses on the delay-dependent stability analysis and stabilization for T-S fuzzy system systems with state and input delays. Some new and less conservative delay-dependent small stability conditions are explicitly obtained. The upper bounds of time-delays are obtained by using small convex optimization.Finally, a numerical example is included to show the effectiveness.

29

Yangjuan, Li, Xiao Zhengying, and Lin Jinzhong. "Stability and Bifurcation of Tumor Immune Model with Time Delay." BIO Web of Conferences 59 (2023): 02017. http://dx.doi.org/10.1051/bioconf/20235902017.

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In this paper, we investigate the effect of time delay on the stability of the tumor immune system using theoretical calculations and numerical simulations. Since it takes a certain time for immune cells to recognize tumor cells to make an appropriate response, a model of tumor-immune system interaction with time delay is established by considering time delay in this process. The four equilibrium points are solved by simplifying the model using Taylor expansion with a small time delay. Then the stability of each equilibrium point of the system under a small time delay is determined by calculating the characteristic roots of each equilibrium point with numerical simulation software. The results show that the system has a bistability phenomenon. The saddle point and stable node are not affected by the delay, while only the stability of the stable foci changes with the time delay with Hopf bifurcation. This study can help determine the optimal time for tumor treatment and provide a reference for analyzing tumor status and treatment.

30

He, Tingyi, Shengnan Li, Shuijun Wu, and Ke Li. "Small-Signal Stability Analysis for Power System Frequency Regulation with Renewable Energy Participation." Mathematical Problems in Engineering 2021 (April 5, 2021): 1–13. http://dx.doi.org/10.1155/2021/5556062.

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With the improvement of the permeability of wind and photovoltaic (PV) energy, it has become one of the key problems to maintain the small-signal stability of the power system. Therefore, this paper analyzes the small-signal stability in a power system integrated with wind and solar energy. First, a mathematical model for small-signal stability analysis of power systems including the wind farm and PV station is established. And the characteristic roots of the New England power system integrated with wind energy and PV energy are obtained to study their small-signal stability. In addition, the validity of the theory is verified by the voltage drop of different nodes, which proves that power system integrated with wind-solar renewable energy participating in the frequency regulation can restore the system to the rated frequency in the shortest time and, at the same time, can enhance the robustness of each unit.

31

Pavlichkov, Svyatoslav. "A small gain theorem for finite-time input-to-state stability of infinite networks and its applications." V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, no. 94 (November 29, 2021): 40–59. http://dx.doi.org/10.26565/2221-5646-2021-94-03.

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We prove a small-gain sufficient condition for (global) finite-time input-to-state stability (FTISS) of infinite networks. The network under consideration is composed of a countable set of finite-dimensional subsystems of ordinary differential equations, each of which is interconnected with a finite number of its “neighbors” only and is affected by some external disturbances. We assume that each node (subsystem) of our network is finite-time input-to-state stable (FTISS) with respect to its finite-dimensional inputs produced by this finite set of the neighbors and with respect to the corresponding external disturbance. As an application we obtain a new theorem on decentralized finite-time input-to-state stabilization with respect to external disturbances for infinite networks composed of a countable set of strict-feedback form systems of ordinary differential equations. For this we combine our small-gain theorem proposed in the current work with the controllers design developed by S. Pavlichkov and C. K. Pang (NOLCOS-2016) for the gain assignment of the strict-feedback form systems in the case of finite networks. The current results address the finite-time input-to-state stability and decentralized finite-time input-to-state stabilization and redesign the technique proposed in recent work S. Dashkovskiy and S. Pavlichkov, Stability conditions for infinite networks of nonlinear systems and their application for stabilization, Automatica. – 2020. – 112. – 108643, in which the case of $\ell_{\infty}$-ISS of infinite networks was investigated. The current paper extends and generalizes its conference predecessor to the case of finite-time ISS stability and decentralized stabilization in presence of external disturbance inputs and with respect to these disturbance inputs. In the special case when all these external disturbances are zeroes (i.e. are abscent), we just obtain finite-time stability and finite-time decentralized stabilization of infinite networks accordingly.

32

Kreiss, Heinz-Otto, and Jens Lorenz. "Stability for time-dependent differential equations." Acta Numerica 7 (January 1998): 203–85. http://dx.doi.org/10.1017/s096249290000283x.

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In this paper we review results on asymptotic stability of stationary states of PDEs. After scaling, our normal form is ut = Pu + ε f(u, ux,…) + F(x, t), where the (vector-valued) function u(x, t) depends on the space variable x and time t. The differential operator P is linear, F(x, t) is a smooth forcing, which decays to zero for t → ∞, and εf(u, …) is a nonlinear perturbation. We will discuss conditions that ensure u → 0 for t → ∞ when |ε| is sufficiently small. If this holds, we call the problem asymptotically stable.While there are many approaches to show asymptotic stability, we mainly concentrate on the resolvent technique. However, comparisons with the Lyapunov technique will also be given. The emphasis on the resolvent technique is motivated by the recent interest in pseudospectra.

33

Davies, M. A., J. R. Pratt, B. Dutterer, and T. J. Burns. "Stability Prediction for Low Radial Immersion Milling." Journal of Manufacturing Science and Engineering 124, no. 2 (April 29, 2002): 217–25. http://dx.doi.org/10.1115/1.1455030.

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Traditional regenerative stability theory predicts a set of optimally stable spindle speeds at integer fractions of the natural frequency of the most flexible mode of the system. The assumptions of this theory become invalid for highly interrupted machining, where the ratio of time spent cutting to not cutting (denoted ρ) is small. This paper proposes a new stability theory for interrupted machining that predicts a doubling in the number of optimally stable speeds as the value of ρ becomes small. The results of the theory are supported by numerical simulation and experiment. It is anticipated that the theory will be relevant for choosing optimal machining parameters in high-speed peripheral milling operations where the radial depth of cut is only a small fraction of the tool diameter.

34

Hsiao, Feng-Hsiag, and Jiing-Dong Hwang. "Stabilization of Nonlinear Singularly Perturbed Multiple Time-Delay Systems by Dither." Journal of Dynamic Systems, Measurement, and Control 118, no. 1 (March 1, 1996): 176–81. http://dx.doi.org/10.1115/1.2801142.

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Dither is a high frequency signal injected into nonlinear systems for the purpose of improving their performance. Stability of the dithered nonlinear singularly perturbed multiple time-delay system is investigated by deriving its corresponding dithered reduced-order model and by using the relaxed method to analyze stability of the dithered reduced-order model when the frequency of dither is sufficiently high. Moreover, if the singular perturbation parameter is sufficiently small, then stability of the relaxed model would imply stability in finite time of the dithered nonlinear singularly perturbed multiple time-delay system.

35

Griffin, Philip S., and Ross A. Maller. "Stability of the exit time for Lévy processes." Advances in Applied Probability 43, no. 3 (September 2011): 712–34. http://dx.doi.org/10.1239/aap/1316792667.

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This paper is concerned with the behaviour of a Lévy process when it crosses over a positive level, u, starting from 0, both as u becomes large and as u becomes small. Our main focus is on the time, τu, it takes the process to transit above the level, and in particular, on the stability of this passage time; thus, essentially, whether or not τu behaves linearly as u ↓ 0 or u → ∞. We also consider the conditional stability of τu when the process drifts to -∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cramér condition.

36

Feola, Roberto, Felice Iandoli, and Federico Murgante. "Long-time stability of the quantum hydrodynamic system on irrational tori." Mathematics in Engineering 4, no. 3 (2021): 1–24. http://dx.doi.org/10.3934/mine.2022023.

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<abstract><p>We consider the quantum hydrodynamic system on a $ d $-dimensional irrational torus with $ d = 2, 3 $. We discuss the behaviour, over a "non-trivial" time interval, of the $ H^s $-Sobolev norms of solutions. More precisely we prove that, for generic irrational tori, the solutions, evolving form $ \varepsilon $-small initial conditions, remain bounded in $ H^s $ for a time scale of order $ O(\varepsilon^{-1-1/(d-1)+}) $, which is strictly larger with respect to the time-scale provided by local theory. We exploit a Madelung transformation to rewrite the system as a nonlinear Schrödinger equation. We therefore implement a Birkhoff normal form procedure involving small divisors arising form three waves interactions. The main difficulty is to control the loss of derivatives coming from the exchange of energy between high Fourier modes. This is due to the irrationality of the torus which prevents to have "good separation'' properties of the eigenvalues of the linearized operator at zero. The main steps of the proof are: (i) to prove precise lower bounds on small divisors; (ii) to construct a modified energy by means of a suitable high/low frequencies analysis, which gives an a priori estimate on the solutions.</p></abstract>

37

Hutt, G. R., R. A. East, and R. D. Wilson. "Large amplitude oscillation effects on cone pitch stability in viscous hypersonic flow." Aeronautical Journal 93, no. 922 (February 1989): 50–57. http://dx.doi.org/10.1017/s0001924000016742.

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SummaryExperimental and theoretical, small and large amplitude stability data are presented for a pointed and a 0.2 bluntness ratio, 10° semi-angle cone performing pitching oscillations in hypersonic flow at a Mach number of 6.85. Analysis identifies that large amplitude model motion time histories cannot be predicted from a knowledge of small amplitude oscillation stability derivatives data. At the Reynolds numbers of the experiments the pointed and blunted cone are subject to significant hypersonic flow viscous phenomena, which are proposed as the cause of the small to large amplitude stability prediction being invalid.

38

Beitia, C., and Y. Borensztein. "Formation and stability of small particles of potassium studied by real-time surface differential reflectance." Surface Science 402-404 (May 1998): 445–49. http://dx.doi.org/10.1016/s0039-6028(98)00004-1.

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39

Logemann, Hartmut, and Richard Rebarber. "The effect of small time-delays on the closed-loop stability of boundary control systems." Mathematics of Control, Signals, and Systems 9, no. 2 (June 1996): 123–51. http://dx.doi.org/10.1007/bf01211750.

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40

Zhang, Xi, Bocheng Bao, Han Bao, Zhimin Wu, and Yihua Hu. "Bi-Stability Phenomenon in Constant On-Time Controlled Buck Converter With Small Output Capacitor ESR." IEEE Access 6 (2018): 46227–32. http://dx.doi.org/10.1109/access.2018.2866124.

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41

Li, Zhicheng, Huijun Gao, and Ramesh K. Agarwal. "Stability analysis and controller synthesis for discrete-time delayed fuzzy systems via small gain theorem." Information Sciences 226 (March 2013): 93–104. http://dx.doi.org/10.1016/j.ins.2012.11.008.

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42

Wang, Guangyu, Lijun Fu, Qi Hu, Chenruiyang Liu, and Yanhong Ma. "Small-signal synchronization stability of grid-forming converter influenced by multi time-scale control interaction." Energy Reports 9 (December 2023): 597–606. http://dx.doi.org/10.1016/j.egyr.2022.11.137.

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43

Liu, Kai. "Almost sure exponential stability sensitive to small time delay of stochastic neutral functional differential equations." Applied Mathematics Letters 77 (March 2018): 57–63. http://dx.doi.org/10.1016/j.aml.2017.09.008.

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44

Maspero, A., and M. Procesi. "Long time stability of small finite gap solutions of the cubic nonlinear Schrödinger equation onT2." Journal of Differential Equations 265, no. 7 (October 2018): 3212–309. http://dx.doi.org/10.1016/j.jde.2018.05.005.

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45

Desogus, Marco, and Beatrice Venturi. "Stability and Bifurcations in Banks and Small Enterprises—A Three-Dimensional Continuous-Time Dynamical System." Journal of Risk and Financial Management 16, no. 3 (March 3, 2023): 171. http://dx.doi.org/10.3390/jrfm16030171.

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Here, we discuss a three-dimensional continuous-time Lotka–Volterra dynamical system, which describes the role of government in interactions with banks and small enterprises. In Italy, during the COVID-19 emergency, the main objective of government economic intervention was to maintain the proper operation of the bank–enterprise system. We also review the effectiveness of measures introduced in response to the COVID-19 pandemic lockdowns to avoid a further credit crunch. By applying bifurcation theory to the system, we were able to produce evidence of the existence of Hopf and zero-Hopf bifurcating periodic solutions from a saddle focus in a special region of the parameter space, and we performed a numerical analysis.

46

Griffin, Philip S., and Ross A. Maller. "Stability of the exit time for Lévy processes." Advances in Applied Probability 43, no. 03 (September 2011): 712–34. http://dx.doi.org/10.1017/s0001867800005115.

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This paper is concerned with the behaviour of a Lévy process when it crosses over a positive level, u, starting from 0, both as u becomes large and as u becomes small. Our main focus is on the time, τ u , it takes the process to transit above the level, and in particular, on the stability of this passage time; thus, essentially, whether or not τ u behaves linearly as u ↓ 0 or u → ∞. We also consider the conditional stability of τ u when the process drifts to -∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cramér condition.

47

Li, Xuemei. "Analysis of Complete Stability for Discrete-Time Cellular Neural Networks with Piecewise Linear Output Functions." Neural Computation 21, no. 5 (May 2009): 1434–58. http://dx.doi.org/10.1162/neco.2008.04-08-744.

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This letter discusses the complete stability of discrete-time cellular neural networks with piecewise linear output functions. Under the assumption of certain symmetry on the feedback matrix, a sufficient condition of complete stability is derived by finite trajectory length. Because the symmetric conditions are not robust, the complete stability of networks may be lost under sufficiently small perturbations. The robust conditions of complete stability are also given for discrete-time cellular neural networks with multiple equilibrium points and a unique equilibrium point. These complete stability results are robust and available.

48

Luján-Soto, Eduardo, and Tzvetanka D. Dinkova. "Time to Wake Up: Epigenetic and Small-RNA-Mediated Regulation during Seed Germination." Plants 10, no. 2 (January 26, 2021): 236. http://dx.doi.org/10.3390/plants10020236.

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Plants make decisions throughout their lifetime based on complex networks. Phase transitions during seed growth are not an exception. From embryo development through seedling growth, several molecular pathways control genome stability, environmental signal transduction and the transcriptional landscape. Particularly, epigenetic modifications and small non-coding RNAs (sRNAs) have been extensively studied as significant handlers of these processes in plants. Here, we review key epigenetic (histone modifications and methylation patterns) and sRNA-mediated regulatory networks involved in the progression from seed maturation to germination, their relationship with seed traits and crosstalk with environmental inputs.

49

CHUNG, HENRY, and ADRIAN IOINOVICI. "LOCAL AND GLOBAL STABILITY OF SWITCHING REGULATORS." Journal of Circuits, Systems and Computers 05, no. 03 (September 1995): 305–15. http://dx.doi.org/10.1142/s0218126695000199.

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A discrete-time model of closed-loop PWM regulators is derived to describe their dynamic behavior. No small-ripple approximations are required. The same model serves both local and global stability study: by discarding the nonlinear terms and using the z-transform, stability for small-signal perturbations is checked; by keeping the nonlinear terms (products of disturbances) and using the state-plane portrait, in which equilibrium points are located, stability for large-signal perturbations is studied. The theory is applied to a multiple feedback boost regulator operating in continuous conduction mode. Its local/global stability/instability for different values of the feedback gains is determined based on the new method.

50

BARREIRA, LUIS, and CLAUDIA VALLS. "Stability of L1 contractions." Mathematical Proceedings of the Cambridge Philosophical Society 159, no. 1 (April 1, 2015): 23–46. http://dx.doi.org/10.1017/s0305004115000158.

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Abstract:

AbstractThe notion of an exponential contraction is only one among many possible rates of contraction of a nonautonomous system, while for an autonomous system all contractions are exponential. We consider the notion of an L1 contraction that includes exponential contractions as a very particular case and that is naturally adapted to the variation-of-parameters formula. Both for discrete and continuous time, we show that under very general assumptions the notion of an L1 contraction persists under sufficiently small linear and nonlinear perturbations, also maintaining the type of stability. As a natural development, we establish a version of the Grobman–Hartman theorem for nonlinear perturbations of an L1 contraction.