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Journal articles on the topic 'Linear singular systems'

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Author: Grafiati

Published: 7 July 2024

Last updated: 7 July 2024

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1

Tolsa, Javier, and Miquel Salichs. "Convergence of singular perturbations in singular linear systems." Linear Algebra and its Applications 251 (January 1997): 105–43. http://dx.doi.org/10.1016/0024-3795(95)00556-0.

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2

Zhang, Naimin, and Yimin Wei. "Solving EP singular linear systems." International Journal of Computer Mathematics 81, no. 11 (November 2004): 1395–405. http://dx.doi.org/10.1080/00207160412331284132.

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3

Bru, R., C. Coll, and N. Thome. "Symmetric singular linear control systems." Applied Mathematics Letters 15, no. 6 (August 2002): 671–75. http://dx.doi.org/10.1016/s0893-9659(02)00026-5.

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4

Carvalho, Cícero F. "Linear systems on singular curves." manuscripta mathematica 98, no. 2 (February 1, 1999): 155–63. http://dx.doi.org/10.1007/s002290050132.

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5

Glizer, Valery Y. "Stability Analysis of Some Types of Singularly Perturbed Time-Delay Differential Systems: Symmetric Matrix Riccati Equation Approach." Symmetry 16, no. 7 (July 3, 2024): 838. http://dx.doi.org/10.3390/sym16070838.

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Several types of linear and nonlinear singularly perturbed time-delay differential systems are considered. Asymptotic stability of the linear systems and asymptotic stability of the trivial solution of the nonlinear systems, valid for any sufficiently small value of the parameter of singular perturbation, are analyzed. For the stability analysis in the linear case, a partial exact slow–fast decomposition of the original system and an application of the Symmetric Matrix Riccati Equation method are proposed. Such an analysis yields parameter-free conditions, providing the asymptotic stability of the considered linear singularly perturbed time-delay differential systems for any sufficiently small value of the parameter of singular perturbation. Using the asymptotic stability results for the considered linear systems and the method of asymptotic stability in the first approximation, parameter-free conditions, guaranteeing the asymptotic stability of the trivial solution to the considered nonlinear systems for any sufficiently small value of the parameter of singular perturbation, are derived. Illustrative examples are presented.

6

Yilin, Chen, Ma Shuping, and Cheng Zhaolin. "Singular optimal control problem of linear singular systems with linear-quadratic cost *." IFAC Proceedings Volumes 32, no. 2 (July 1999): 2887–92. http://dx.doi.org/10.1016/s1474-6670(17)56492-7.

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7

Mironovskii, L. A. "Linear systems with multiple singular values." Automation and Remote Control 70, no. 1 (January 2009): 43–63. http://dx.doi.org/10.1134/s0005117909010044.

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8

Wei, Y. "Perturbation bound of singular linear systems." Applied Mathematics and Computation 105, no. 2-3 (November 1999): 211–20. http://dx.doi.org/10.1016/s0096-3003(99)00120-4.

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9

Du, Xiuhong, and Daniel B. Szyld. "Inexact GMRES for singular linear systems." BIT Numerical Mathematics 48, no. 3 (July 5, 2008): 511–31. http://dx.doi.org/10.1007/s10543-008-0171-2.

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10

Heck, B. S., and A. H. Haddad. "Singular perturbation in piecewise-linear systems." IEEE Transactions on Automatic Control 34, no. 1 (1989): 87–90. http://dx.doi.org/10.1109/9.8652.

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11

Novo, Sylvia, and Rafael Obaya. "Bidimensional linear systems with singular dynamics." Proceedings of the American Mathematical Society 124, no. 10 (1996): 3163–72. http://dx.doi.org/10.1090/s0002-9939-96-03411-9.

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12

Lewis, F. L. "A survey of linear singular systems." Circuits, Systems, and Signal Processing 5, no. 1 (March 1986): 3–36. http://dx.doi.org/10.1007/bf01600184.

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13

Notay, Yvan. "Incomplete factorizations of singular linear systems." BIT 29, no. 4 (December 1989): 682–702. http://dx.doi.org/10.1007/bf01932740.

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14

Grispos, E., G. Kalogeropoulos, and I. G. Stratis. "On Generalized Linear Singular Delay Systems." Journal of Mathematical Analysis and Applications 245, no. 2 (May 2000): 430–46. http://dx.doi.org/10.1006/jmaa.2000.6761.

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15

Kaczorek, Tadeusz. "Singular fractional linear systems and electrical circuits." International Journal of Applied Mathematics and Computer Science 21, no. 2 (June 1, 2011): 379–84. http://dx.doi.org/10.2478/v10006-011-0028-8.

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Singular fractional linear systems and electrical circuitsA new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.

16

Nikuie, M., and M. Z. Ahmad. "Minimal Solution of Singular LR Fuzzy Linear Systems." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/517218.

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In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.

17

Yoo, Heonjong, Zoran Gajic, and Kyeong-Hwan Lee. "Reduced-Order Algorithm for Eigenvalue Assignment of Singularly Perturbed Linear Systems." Mathematical Problems in Engineering 2020 (May 30, 2020): 1–10. http://dx.doi.org/10.1155/2020/3948564.

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In this paper, we present an algorithm for eigenvalue assignment of linear singularly perturbed systems in terms of reduced-order slow and fast subproblem matrices. No similar algorithm exists in the literature. First, we present an algorithm for the recursive solution of the singularly perturbed algebraic Sylvester equation used for eigenvalue assignment. Due to the presence of a small singular perturbation parameter that indicates separation of the system variables into slow and fast, the corresponding algebraic Sylvester equation is numerically ill-conditioned. The proposed method for the recursive reduced-order solution of the algebraic Sylvester equations removes ill-conditioning and iteratively obtains the solution in terms of four reduced-order numerically well-conditioned algebraic Sylvester equations corresponding to slow and fast variables. The convergence rate of the proposed algorithm is Oε, where ε is a small positive singular perturbation parameter.

18

Kaczorek, Tadeusz. "SINGULAR FRACTIONAL CONTINUOUS-TIME AND DISCRETE-TIME LINEAR SYSTEMS." Acta Mechanica et Automatica 7, no. 1 (March 1, 2013): 26–33. http://dx.doi.org/10.2478/ama-2013-0005.

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Abstract New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.

19

AZARFAR, Azita, Heydar Toossian SHANDIZ, and Masoud SHAFIEE. "Adaptive feedback control for linear singular systems." TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES 22 (2014): 132–42. http://dx.doi.org/10.3906/elk-1207-55.

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20

Zhou, Jieyong, and Zhenyu Zhang. "Solving large scale fuzzy singular linear systems." Journal of Intelligent & Fuzzy Systems 35, no. 1 (July 27, 2018): 601–7. http://dx.doi.org/10.3233/jifs-15689.

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21

Meng, B., and J. F. Zhang. "Reachability Conditions for Switched Linear Singular Systems." IEEE Transactions on Automatic Control 51, no. 3 (March 2006): 482–88. http://dx.doi.org/10.1109/tac.2005.864196.

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22

BAHI, J. "PARALLEL CHAOTIC ALGORITHMS FOR SINGULAR LINEAR SYSTEMS." Parallel Algorithms and Applications 14, no. 1 (May 1999): 19–35. http://dx.doi.org/10.1080/10637199808947376.

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23

Ayala, Victor, and Philippe Jouan. "Singular linear systems on Lie groups; equivalence." Systems & Control Letters 120 (October 2018): 1–8. http://dx.doi.org/10.1016/j.sysconle.2018.07.010.

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24

Ballico, E. "Singular bielliptic curves and special linear systems." Journal of Pure and Applied Algebra 162, no. 2-3 (August 2001): 171–82. http://dx.doi.org/10.1016/s0022-4049(00)00130-4.

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25

Shcheglova, Alla A. "On observability of singular linear hybrid systems." Nonlinear Analysis: Theory, Methods & Applications 62, no. 8 (September 2005): 1419–36. http://dx.doi.org/10.1016/j.na.2005.02.120.

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26

Zhou, Lei, Daniel W. C. Ho, and Guisheng Zhai. "Stability analysis of switched linear singular systems." Automatica 49, no. 5 (May 2013): 1481–87. http://dx.doi.org/10.1016/j.automatica.2013.02.002.

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27

DIEZ-MACHÍO, H., J. CLOTET, M. I. GARCÍA-PLANAS, M. D. MAGRET, and M. E. MONTORO. "SINGULAR SWITCHED LINEAR SYSTEMS: SOME GEOMETRIC ASPECTS." International Journal of Modern Physics B 26, no. 25 (September 10, 2012): 1246006. http://dx.doi.org/10.1142/s021797921246006x.

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We present a geometric approach to the study of singular switched linear systems, defining a Lie group action on the differentiable manifold consisting of the matrices defining their subsystems with orbits coinciding with equivalence classes under an equivalence relation which preserves reachability and derive miniversal (orthogonal) deformations of the system. We relate this with some new results on reachability of such systems.

28

HAN, JEN-YIN, and CHIN-YUAN LIN. "POWER SERIES SOLUTIONS OF SINGULAR LINEAR SYSTEMS." International Journal of Mathematics 23, no. 02 (February 2012): 1250034. http://dx.doi.org/10.1142/s0129167x12500346.

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29

Dai, Liyi. "INPUT FUNCTION OBSERVERS FOR LINEAR SINGULAR SYSTEMS." Acta Mathematica Scientia 9, no. 3 (September 1989): 337–46. http://dx.doi.org/10.1016/s0252-9602(18)30358-8.

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30

DAROUACH, M., M. ZASADZINSKI, and D. MEHDI. "State estimation of stochastic singular linear systems." International Journal of Systems Science 24, no. 2 (February 1993): 345–54. http://dx.doi.org/10.1080/00207729308949493.

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31

Hager, William W. "Iterative Methods for Nearly Singular Linear Systems." SIAM Journal on Scientific Computing 22, no. 2 (January 2000): 747–66. http://dx.doi.org/10.1137/s106482759834634x.

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32

CHRISTODOULOU, MANOLIS A., and CAN ISIK. "Feedback control for non-linear singular systems." International Journal of Control 51, no. 2 (January 1990): 487–94. http://dx.doi.org/10.1080/00207179008934076.

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33

Boukas, E. K. "Singular linear systems with delay: ℋ∞ stabilization." Optimal Control Applications and Methods 28, no. 4 (2007): 259–74. http://dx.doi.org/10.1002/oca.801.

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34

Kodra, Kliti, Maja Skataric, and Zoran Gajic. "Finding Hankel singular values for singularly perturbed linear continuous-time systems." IET Control Theory & Applications 11, no. 7 (April 25, 2017): 1063–69. http://dx.doi.org/10.1049/iet-cta.2016.1240.

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35

Mu¨ller, Peter C. "Stability of Linear Mechanical Systems With Holonomic Constraints." Applied Mechanics Reviews 46, no. 11S (November 1, 1993): S160—S164. http://dx.doi.org/10.1115/1.3122633.

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Singular systems (descriptor systems, differential-algebraic equations) are a recent topic of research in numerical mathematics, mechanics and control theory as well. But compared with common methods available for investigating regular systems many problems still have to be solved making also available a complete set of tools to analyze, to design and to simulate singular systems. In this contribution the aspect of stability is considered. Some new results for linear singular systems are presented based on a generalized Lyapunov matrix equation. Particularly, for mechanical systems with holonomic constraints the well-known stability theorem of Thomson and Tait is generalized.

36

Feng, Jun-e., Peng Cui, and Zhongsheng Hou. "Singular linear quadratic optimal control for singular stochastic discrete-time systems." Optimal Control Applications and Methods 34, no. 5 (May 9, 2012): 505–16. http://dx.doi.org/10.1002/oca.2033.

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37

Rehman, Mutti-Ur, Jehad Alzabut, Nahid Fatima, and Tulkin H. Rasulov. "The Stability Analysis of Linear Systems with Cauchy—Polynomial-Vandermonde Matrices." Axioms 12, no. 9 (August 28, 2023): 831. http://dx.doi.org/10.3390/axioms12090831.

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The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein–Vandermonde matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi-rational Bernstein–Vandermonde structured matrices are well studied and investigated in the literature. We aim to present some new results for the numerical approximation of the largest singular values corresponding to Bernstein–Vandermonde, Bernstein–Bezoutian, Cauchy—polynomial-Vandermonde and quasi-rational Bernstein–Vandermonde structured matrices. The numerical approximation for the reciprocal of the largest singular values returns the structured singular values. The new results for the numerical approximation of bounds from below for structured singular values are accomplished by computing the largest singular values of totally positive Bernstein–Vandermonde structured matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and quasi-rational Bernstein–Vandermonde structured matrices. Furthermore, we present the spectral properties of totally positive Bernstein–Vandermonde structured matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matrices, and structured quasi-rational Bernstein–Vandermonde matrices by computing the eigenvalues, singular values, structured singular values and its lower and upper bounds and condition numbers.

38

Rehman, Mutti-Ur, Jehad Alzabut, and Muhammad Fazeel Anwar. "Stability Analysis of Linear Feedback Systems in Control." Symmetry 12, no. 9 (September 15, 2020): 1518. http://dx.doi.org/10.3390/sym12091518.

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This article presents a stability analysis of linear time invariant systems arising in system theory. The computation of upper bounds of structured singular values confer the stability analysis, robustness and performance of feedback systems in system theory. The computation of the bounds of structured singular values of Toeplitz and symmetric Toeplitz matrices for linear time invariant systems is presented by means of low rank ordinary differential equations (ODE’s) based methodology. The proposed methodology is based upon the inner-outer algorithm. The inner algorithm constructs and solves a gradient system of ODE’s while the outer algorithm adjusts the perturbation level with fast Newton’s iteration. The comparison of bounds of structured singular values approximated by low rank ODE’s based methodology results tighter bounds when compared with well-known MATLAB routine mussv, available in MATLAB control toolbox.

39

Wang, Mengdi, and Dimitri P. Bertsekas. "Stabilization of Stochastic Iterative Methods for Singular and Nearly Singular Linear Systems." Mathematics of Operations Research 39, no. 1 (February 2014): 1–30. http://dx.doi.org/10.1287/moor.2013.0596.

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40

Zhou, Haiying, Huainian Zhu, and Chengke Zhang. "Linear Quadratic Nash Differential Games of Stochastic Singular Systems." Journal of Systems Science and Information 2, no. 6 (December 25, 2014): 553–60. http://dx.doi.org/10.1515/jssi-2014-0553.

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AbstractIn this paper, we deal with the Nash differential games of stochastic singular systems governed by Itô-type equation in finite-time horizon and infinite-time horizon, respectively. Firstly, the Nash differential game problem of stochastic singular systems in finite time horizon is formulated. By applying the results of stochastic optimal control problem, the existence condition of the Nash strategy is presented by means of a set of cross-coupled Riccati differential equations. Similarly, under the assumption of the admissibility of the stochastic singular systems, the existence condition of the Nash strategy in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. The results show that the strategies of each players interact.

41

Dassios, Ioannis, Georgios Tzounas, Muyang Liu, and Federico Milano. "Singular over-determined systems of linear differential equations." Mathematics and Computers in Simulation 197 (July 2022): 396–412. http://dx.doi.org/10.1016/j.matcom.2022.02.003.

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42

Yu, Wenxin, Yigang He, Xianming Wu, and Kun Gao. "Controllability of Singular Linear Systems by Legendre Wavelets." Journal of Control Science and Engineering 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/573959.

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We propose a new method to design an observer and control the linear singular systems described by Legendre wavelets. The idea of the proposed approach is based on solving the generalized Sylvester equations. An example is also given to illustrate the procedure.

43

Yan, Zhibin, and Guangren Duan. "Impulse Analysis of Linear Time-Varying Singular Systems." IEEE Transactions on Automatic Control 51, no. 12 (December 2006): 1975–79. http://dx.doi.org/10.1109/tac.2006.886500.

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44

Yu, Wenxin, Yigang He, Kun Gao, and Xianming Wu. "Controllability of singular linear systems by Legendre wavelets." International Journal of Information and Communication Technology 10, no. 2 (2017): 185. http://dx.doi.org/10.1504/ijict.2017.082079.

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45

Yu, Wenxin, Yigang He, Xianming Wu, and Kun Gao. "Controllability of singular linear systems by Legendre wavelets." International Journal of Information and Communication Technology 10, no. 2 (2017): 185. http://dx.doi.org/10.1504/ijict.2017.10002122.

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46

Sun, Huaqing, and Yuming Shi. "Spectral properties of singular discrete linear Hamiltonian systems." Journal of Difference Equations and Applications 20, no. 3 (August 27, 2013): 379–405. http://dx.doi.org/10.1080/10236198.2013.824432.

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47

Evans, David J., K. Murugesan, S. Sekar, and Hyun-Min Kim. "Non-linear singular systems using RK–Butcher algorithms." International Journal of Computer Mathematics 83, no. 1 (January 2006): 131–42. http://dx.doi.org/10.1080/00207160500069888.

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48

Sun, Huaqing, and Yuming Shi. "On essential spectra of singular linear Hamiltonian systems." Linear Algebra and its Applications 469 (March 2015): 204–29. http://dx.doi.org/10.1016/j.laa.2014.11.030.

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49

Gaidomak, S. V. "Spline collocation method for linear singular hyperbolic systems." Computational Mathematics and Mathematical Physics 48, no. 7 (July 2008): 1161–80. http://dx.doi.org/10.1134/s0965542508070099.

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50

Chuanguo, Chen, Ma Shuping, and Cheng Zhaolin. "The output regulation problem of linear singular systems." IFAC Proceedings Volumes 32, no. 2 (July 1999): 1612–17. http://dx.doi.org/10.1016/s1474-6670(17)56273-4.

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