Invariance principles for hybrid systems with memory

被引：11

作者：

Liu, Jun ^{[1
]}

Teel, Andrew R. ^{[2
]}

机构：

[1] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

[2] Univ Calif Santa Barbara, Dept Elect & Comp Engn, Santa Barbara, CA 93106 USA

来源：

NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2016年 / 21卷

基金：

美国国家科学基金会;

关键词：

Hybrid systems with memory; Hybrid functional inclusions; Invariance principles; Stability; FUNCTIONAL-DIFFERENTIAL EQUATIONS; UNIFORM ASYMPTOTIC STABILITY; DYNAMICAL-SYSTEMS; SWITCHED SYSTEMS; TIME-DELAY;

D O I：

10.1016/j.nahs.2015.08.003

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Hybrid systems with memory are dynamical systems exhibiting both delayed and hybrid dynamics. Such systems can be described by hybrid functional inclusions. Classical invariance principles play an instrumental role in proving stability and convergence of dynamical systems. Invariance principles for general hybrid systems with delays, however, remain an open topic. In this paper, we prove invariance principles for hybrid systems with memory, using both Lyapunov-Razumikhin function and Lyapunov-Krasovskii functional methods. These invariance principles are then applied to derive two stability results as corollaries. (C) 2016 Published by Elsevier Ltd.

引用

页码：130 / 138

页数：9

共 26 条

[1] An invariance principle for nonlinear switched systems
Bacciotti, A
Mazzi, L
[J]. SYSTEMS & CONTROL LETTERS, 2005, 54 (11) : 1109 - 1119
[2] An invariance principle for nonlinear hybrid and impulsive dynamical systems
Chellaboina, V
Bhat, SP
Haddad, WM
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 53 (3-4) : 527 - 550
[3] Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays
Chen, Wu-Hua
Zheng, Wei Xing
[J]. AUTOMATICA, 2009, 45 (06) : 1481 - 1488
[4] Invariance principles for switching systems via hybrid systems techniques
Goebel, Rafal
Sanfelice, Ricardo G.
Teel, Andrew R.
[J]. SYSTEMS & CONTROL LETTERS, 2008, 57 (12) : 980 - 986
[5] Goebel Rafal, 2012, Hybrid dynamical systems
[6] LIAPUNOV-RAZUMIKHIN FUNCTIONS AND AN INVARIANCE-PRINCIPLE FOR FUNCTIONAL-DIFFERENTIAL EQUATIONS
HADDOCK, JR
TERJEKI, J
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1983, 48 (01) : 95 - 122
[7] SUFFICIENT CONDITIONS FOR STABILITY AND INSTABILITY OF AUTONOMOUS FUNCTIONAL-DIFFERENTIAL EQUATIONS
HALE, JK
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1965, 1 (04) : 452 - &
[8] Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle
Hespanha, JP
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (04) : 470 - 482
[9] LaSalle J., 1960, IRE Transactions on Circuit Theory, V7, P520, DOI [DOI 10.1109/TCT.1960.1086720, 10.1109/TCT.1960.1086720]
[10] THE EXTENT OF ASYMPTOTIC STABILITY
LASALLE, JP
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1960, 46 (03) : 363 - 365

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