Lyapunov-Based Sufficient Conditions for Stability of Hybrid Systems With Memory

被引：32

作者：

Liu, Jun ^{[1
]}

Teel, Andrew R. ^{[2
,3
]}

机构：

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

[2] Univ Calif Santa Barbara, Ctr Control Dynam Syst & Computat, Santa Barbara, CA 93106 USA

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

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 04期

基金：

美国国家科学基金会;

关键词：

Functional inclusions; generalized solutions; hybrid systems; stability; time delay; UNIFORM ASYMPTOTIC STABILITY; GENERALIZED SOLUTIONS; DYNAMICAL-SYSTEMS;

D O I：

10.1109/TAC.2015.2460031

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 hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions, motivated by studying robustness and well-posedness of such systems, are defined on hybrid time domains and parameterized by both continuous and discrete time. We establish Lyapunov-based sufficient conditions for asymptotic stability using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals. Examples are provided to illustrate these conditions.

引用

页码：1057 / 1062

页数：6

共 22 条

[1]

[Anonymous], 1993, INTRO FUNCTIONAL DIF

[2]

Banos A, 2014, LOW COMPLEXITY CONTR, P111

[3] Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays [J].

Chen, Wu-Hua ;

Zheng, Wei Xing .

AUTOMATICA, 2009, 45 (06) :1481-1488

[4] Tractable Razumikhin-type conditions for input-to-state stability analysis of delay difference inclusions [J].

Gielen, R. H. ;

Teel, A. R. ;

Lazar, M. .

AUTOMATICA, 2013, 49 (02) :619-625

[5] Necessary and Sufficient Razumikhin-Type Conditions for Stability of Delay Difference Equations [J].

Gielen, Rob H. ;

Lazar, Mircea ;

Rakovic, Sasa V. .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2013, 58 (10) :2637-2642

[6]

Goebel R., 2004, 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2004), P1

[7] Solutions to hybrid inclusions via set and graphical convergence with stability theory applications [J].

Goebel, R ;

Teel, AR .

AUTOMATICA, 2006, 42 (04) :573-587

[8]

Goebel Rafal, 2012, Hybrid dynamical systems

[9]

Halanay A., 1966, Differential equations: stability, oscillations, time lags, volume 23 of Mathematics in Science and Engineering, V23

[10]

Khalil H. K., 1992, NONLINEAR SYSTEMS

← 1 2 3 →