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Journal articles on the topic 'Linear singular systems'

Author: Grafiati

Published: 7 July 2024

Last updated: 19 July 2025

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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 (2004): 1395–405. http://dx.doi.org/10.1080/00207160412331284132.

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3

Allahverdiev, Bilender, and Huseyin Tuna. "Singular linear q-Hamiltonian systems." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 78, no. 1 (2024): 1–15. https://doi.org/10.17951/a.2024.78.1.1-15.

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In this paper, a singular linear q-Hamiltonian system is considered. The Titchmarsh-Weyl theory for this problem is constructed. Firstly, we provide some necessary fundamental concepts of the q-calculus. Later, we studied Titchmarsh-Weyl functions M(λ) and circles CTW(a,λ) for this system. Circles CTW(a,λ) are proved to be nested. In the fourth part of the work, the number of square-integrable solutions of this system is studied. In the fifth part of the work, boundary conditions in the singular case are obtained. Finally, a self-adjoint operator is defined.

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4

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

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5

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

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6

Glizer, Valery Y. "Stability Analysis of Some Types of Singularly Perturbed Time-Delay Differential Systems: Symmetric Matrix Riccati Equation Approach." Symmetry 16, no. 7 (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

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7

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 (1999): 2887–92. http://dx.doi.org/10.1016/s1474-6670(17)56492-7.

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8

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.

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9

Kaczorek, Tadeusz. "Singular fractional linear systems and electrical circuits." International Journal of Applied Mathematics and Computer Science 21, no. 2 (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 supercoil

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10

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

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11

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

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12

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

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13

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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14

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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15

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

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16

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

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17

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

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18

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 r

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19

Kaczorek, Tadeusz. "SINGULAR FRACTIONAL CONTINUOUS-TIME AND DISCRETE-TIME LINEAR SYSTEMS." Acta Mechanica et Automatica 7, no. 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

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20

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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21

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

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22

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

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23

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

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24

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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25

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

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26

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

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27

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

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28

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 (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.

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29

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

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30

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

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31

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

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32

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

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33

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

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34

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

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35

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 (2017): 1063–69. http://dx.doi.org/10.1049/iet-cta.2016.1240.

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36

Mu¨ller, Peter C. "Stability of Linear Mechanical Systems With Holonomic Constraints." Applied Mechanics Reviews 46, no. 11S (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 holono

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37

Titova, Tatiana. "Canonical transformations of linear Hamiltonian systems." E3S Web of Conferences 592 (2024): 04009. http://dx.doi.org/10.1051/e3sconf/202459204009.

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In this paper we consider the linear Hamiltonian systems of differential equations. We explore the normalization of a non-singular Hamiltonian matrix. We solve a system of matrix equations to find the generating function of the canonical transformation. In various cases we obtain the solution of the system of matrix equations. We get the solution of the algebraic matrix Riccati equation under certain conditions. Some properties of the Hamiltonian matrix have been proven. We get the normal form of a non-singular Hamiltonian matrix of order 4. We obtain the new method of normalization of the qua

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38

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 (2012): 505–16. http://dx.doi.org/10.1002/oca.2033.

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39

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 (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

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40

Rehman, Mutti-Ur, Jehad Alzabut, and Muhammad Fazeel Anwar. "Stability Analysis of Linear Feedback Systems in Control." Symmetry 12, no. 9 (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

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41

Packard, Andy, John Doyle та Gary Balas. "Linear, Multivariable Robust Control With a μ Perspective". Journal of Dynamic Systems, Measurement, and Control 115, № 2B (1993): 426–38. http://dx.doi.org/10.1115/1.2899083.

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The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. Th

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42

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 (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 conditi

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43

Zamani, Iman, Masoud Shafiee, Mohsen Shafieirad, and Mahdi Zeinali. "Optimal control of large-scale singular linear systems via hierarchical strategy." Transactions of the Institute of Measurement and Control 41, no. 8 (2018): 2250–67. http://dx.doi.org/10.1177/0142331218796553.

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This paper states a hierarchical strategy of large-scale singular linear system in which the system is composed of J singular linear subsystems with interconnections. Among hierarchical strategies, the two-level optimization conditions based on Interaction Prediction Method (IPM) are derived such that whole large-scale singular system is optimized. Based on the two-level coordination method, the optimization analysis and controller design of large-scale singular linear system is discussed. For this purpose, two decentralized nonlinear state feedback controllers are designed for each subsystem,

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44

Glizer, Valery. "Euclidean Space Controllability Conditions for Singularly Perturbed Linear Systems with Multiple State and Control Delays." Axioms 8, no. 1 (2019): 36. http://dx.doi.org/10.3390/axioms8010036.

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A singularly perturbed linear time-dependent controlled system with multiple point-wise delays and distributed delays in the state and control variables is considered. The delays are small, of order of a small positive multiplier for a part of the derivatives in the system. This multiplier is a parameter of the singular perturbation. Two types of the considered singularly perturbed system, standard and nonstandard, are analyzed. For each type, two much simpler parameter-free subsystems (the slow and fast ones) are associated with the original system. It is established in the paper that proper

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45

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 (2014): 1–30. http://dx.doi.org/10.1287/moor.2013.0596.

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46

Yang, Bohui, Ziyang Luo, Xindong Zhang, Quan Tang, and Juan Liu. "Trajectories and Singular Points of Two-Dimensional Fractional-Order Autonomous Systems." Advances in Mathematical Physics 2022 (July 28, 2022): 1–9. http://dx.doi.org/10.1155/2022/3722011.

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In this paper, we study the trajectories and singular points of two-dimensional fractional-order planar autonomous linear system involving the Caputo-Fabrizio fractional derivative. By the corresponding fractional integral of the Caputo-Fabrizio fractional derivative, we obtain the analytical solutions for the fractional-order planar autonomous linear system, and then, we discuss the behavior of the trajectories for the mentioned autonomous linear system. Furthermore, we consider the existence of singular points in the trajectories. We discuss the conditions under which the singular point is s

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47

Kaczorek, T. "Positive fractional continuous-time linear systems with singular pencils." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 1 (2012): 9–12. http://dx.doi.org/10.2478/v10175-012-0002-0.

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Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

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48

Chen, Chao Tian, and Jin Lun Ding. "The Stabilization of Singular Linear Large-Scale Control Systems with Output Feedbacks." Advanced Materials Research 383-390 (November 2011): 72–78. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.72.

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The stabilization problem of singular linear large-scale control systems with output feedbacks is investigated by using the generalized Lyapunov matrix equation, system decomposition method, singular systems theory and matrix theory. Some sufficient conditions for determining the asymptotical stability and unstability of the corresponding singular closed-loop large-scale systems are given. At last, an illustrate example is given to show the application of main result.

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49

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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50

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.

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