On Stability of Switched Discrete-Time Singular Systems

被引:0
|
作者
Raj, Phani [1 ]
Pal, Debasattam [1 ]
机构
[1] Indian Inst Technol, Dept Elect Engn, Mumbai 400076, India
关键词
Switches; Algebra; Stability criteria; Lyapunov methods; Sufficient conditions; Switched systems; Power system stability; Discrete-time systems; Lie algebraic criteria for stability; stability of switched systems; switched singular systems; DESCRIPTOR SYSTEMS; EQUATIONS; DESIGN;
D O I
10.1109/TAC.2024.3396392
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this article, we prove multiple criteria for the stability of switched discrete-time linear singular (SDLS) systems. First, we show that if the Lie algebra generated by the flow matrices associated with an SDLS system, consisting of stable subsystems, is solvable, then the SDLS system is globally uniformly exponentially stable. Most results in the literature are based on commutativity and the Lie algebraic results of this note generalize the existing results. Furthermore, using the first result, we prove a Lie algebraic criterion involving the system matrices. We also prove a Lyapunov function-based sufficient condition for the exponential stability of SDLS systems and show that this result is equivalent to the existing Lyapunov function-based sufficient condition in the literature. Using this result, we show that an SDLS system with a common descriptor matrix satisfying the Lie algebraic criterion admits a common quadratic Lyapunov function. Finally, we extend the commutativity-based result for SDLS systems involving two subsystems and a common descriptor matrix in the literature to SDLS systems involving finitely many, but arbitrary number of subsystems.
引用
收藏
页码:7112 / 7119
页数:8
相关论文
共 50 条
  • [1] Research on Stability for Discrete-time Switched Linear Singular Systems
    Men Bo
    Yu Xinyang
    Zhang Qingling
    [J]. 2010 CHINESE CONTROL AND DECISION CONFERENCE, VOLS 1-5, 2010, : 2459 - +
  • [2] Stability of periodically switched discrete-time linear singular systems
    Pham Ky Anh
    Pham Thi Linh
    [J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2017, 23 (10) : 1680 - 1693
  • [3] Stability analysis for switched discrete-time linear singular systems
    Pham Ky Anh
    Pham Thi Linh
    Do Duc Thuan
    Trenn, Stephan
    [J]. AUTOMATICA, 2020, 119
  • [4] Stability and stabilizability of positive switched discrete-time linear singular systems
    Thuan, Do Duc
    Thu, Ninh Thi
    [J]. SYSTEMS & CONTROL LETTERS, 2024, 185
  • [5] On stability of discrete-time switched systems
    Kundu, Atreyee
    Chatterjee, Debasish
    [J]. NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2017, 23 : 191 - 210
  • [6] Input-to-state stability for discrete-time nonlinear switched singular systems
    Liu, Yunlong
    Kao, Yonggui
    Karimi, Hamid Reza
    Gao, Zairui
    [J]. INFORMATION SCIENCES, 2016, 358 : 18 - 28
  • [7] Admissibility and control of switched discrete-time singular systems
    Darouach, M.
    Chadli, M.
    [J]. SYSTEMS SCIENCE & CONTROL ENGINEERING, 2013, 1 (01) : 43 - 51
  • [8] Quadratic stability of discrete-time switched systems
    Li, Chunming
    Liu, Xiaohua
    [J]. CISP 2008: FIRST INTERNATIONAL CONGRESS ON IMAGE AND SIGNAL PROCESSING, VOL 5, PROCEEDINGS, 2008, : 563 - 565
  • [9] Stability and stabilization in switched discrete-time systems
    Zhang, Hui
    Shi, Yang
    Mehr, Aryan Saadat
    [J]. INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, 2012, 26 (11) : 991 - 1012
  • [10] Uniform finite-time stability for a class of uncertain discrete-time switched singular systems
    [J]. Yang, K. (ytyangkun@163.com), 1600, Chinese Institute of Electronics (35):