Lyapunov Functions, Stability and Input-to-State Stability Subtleties for Discrete-Time Discontinuous Systems

被引：48

作者：

Lazar, Mircea ^{[1
]}

Heemels, W. P. Maurice H. ^{[2
]}

Teel, Andy R. ^{[3
]}

机构：

[1] Eindhoven Univ Technol, Dept Elect Engn, NL-5600 MB Eindhoven, Netherlands

[2] Eindhoven Univ Technol, Dept Mech Engn, NL-5600 MB Eindhoven, Netherlands

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

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2009年 / 54卷 / 10期

关键词：

Discontinuous systems; discrete-time; input-to-state stability; Lyapunov methods; stability; MODEL-PREDICTIVE CONTROL; HYBRID SYSTEMS; PIECEWISE AFFINE; STABILIZATION;

D O I：

10.1109/TAC.2009.2029297

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 note we consider stability analysis of discrete-time discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov is precarious for discrete-time discontinuous dynamics. Also, we indicate that a particular type of Lyapunov condition, slightly stronger than the classical one, is required to establish stability of discrete-time discontinuous systems. Furthermore, we examine the robustness of the stability property when it was attained via a discontinuous Lyapunov function, which is often the case for discrete-time hybrid systems. In contrast to existing results based on smooth Lyapunov functions, we develop several input-to-state stability tests that explicitly employ an available discontinuous Lyapunov function.

引用

页码：2421 / 2425

页数：5