The Set of Asymptotically Stable Switching Sequences of Linear Discrete-Time Switching Systems

被引：0

作者：

Huang, Yu ^{[1
]}

Luo, Jun ^{[1
]}

Huang, Tingwen ^{[2
]}

Xiao, MingQing ^{[3
]}

机构：

[1] Zhongshan Univ, Guangzhou, Guangdong, Peoples R China

[2] Texas A&M Univ, Doha, Qatar

[3] Southern Illinois Univ, Carbondale, IL 62901 USA

来源：

PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009) | 2009年

关键词：

Discrete-time switched linear systems; asymptotically stability; Hausdorff dimension; ergodic probability measure; LYAPUNOV FUNCTIONS; STABILITY ANALYSIS; DYNAMICAL-SYSTEMS; STABILIZATION;

D O I：

10.1109/CDC.2009.5399807

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 paper we study the characterization of asymptotic stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension of the set of asymptotically stable switching sequences is positive if and only if the corresponding switched linear system has at least one asymptotically stable switching sequence. The obtained result reveals a underlying fundamental principle: a switched linear system either possesses uncountable numbers of asymptotically stable switching sequences or has none of them, provided that the switching is arbitrary.

引用

页码：2162 / 2167

页数：6

共 50 条

[31] A STABILITY DICHOTOMY FOR DISCRETE-TIME LINEAR SWITCHING SYSTEMS IN DIMENSION TWO
Morris, Ian d.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2024, 62 (01) : 400 - 414
[32] Output feedback controller design of discrete-time linear switching systems
Fan, Guowei
Liu, Zhiyuan
Chen, Hong
Jin, Guang
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2014, 36 (01) : 47 - 57
[33] Stabilization of Discrete-Time Nonlinear Switching Systems
Benmessaouda, Ouahiba
Benzaouia, Abdellah
CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2014, 33 (10) : 3277 - 3286
[34] Stabilization of Discrete-Time Nonlinear Switching Systems
Ouahiba Benmessaouda
Abdellah Benzaouia
Circuits, Systems, and Signal Processing, 2014, 33 : 3277 - 3286
[35] Quadratic Filtering for non-Gaussian and not Asymptotically Stable Linear Discrete-Time Systems
Cacace, Filippo
Conte, Francesco
Germani, Alfredo
Palombo, Giovanni
2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2014, : 4995 - 5000
[36] Dwell-Time Min-Switching for Discrete-time Switched Linear Systems
Duan, Chang
Wu, Fen
2014 EUROPEAN CONTROL CONFERENCE (ECC), 2014, : 2540 - 2545
[37] Switching controller synthesis for discrete-time switched linear systems with average dwell time
He, Wei
Xie, Wei
Wu, Weilin
Zhagn, Langwen
ARCHIVES OF CONTROL SCIENCES, 2020, 30 (01) : 5 - 22
[38] Dynamic Feedforward Compensation of Measurable Signals in Discrete-Time Linear Switching Systems
Zattoni, Elena
2013 AMERICAN CONTROL CONFERENCE (ACC), 2013, : 848 - 853
[39] Robust stabilizing controller design for the uncertain discrete-time linear switching systems
Fan, Guowei
2013 THIRD INTERNATIONAL CONFERENCE ON INSTRUMENTATION & MEASUREMENT, COMPUTER, COMMUNICATION AND CONTROL (IMCCC), 2013, : 1684 - 1688
[40] Maximum-likelihood Kalman Filtering for Switching Discrete-time Linear Systems
Alessandri, A.
Baglietto, M.
Battistelli, G.
47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, : 3192 - 3198

← 1 2 3 4 5 →