On formalism and stability of switched systems

被引：13

作者：

Leth J. ^{[1
]}

Wisniewski R. ^{[1
]}

机构：

[1] Department of Electronic Systems, Automation and Control, Aalborg University, 9220 Aalborg East

来源：

Journal of Control Theory and Applications | 2012年 / 10卷 / 02期

关键词：

Differential inclusions; Inertia; Quadratic forms; Stability; Switched systems;

D O I：

10.1007/s11768-012-0138-3

中图分类号：

学科分类号：

摘要：

In this paper, we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching. Based on known results from the theory of differential inclusions, we devise a Lyapunov stability theorem suitable for this class of switched systems. With this, we prove a Lyapunov stability theorem for piecewise linear switched systems by means of a concrete class of Lyapunov functions. Contrary to existing results on the subject, the stability theorems in this paper include Filippov (or relaxed) solutions and allow infinite switching in finite time. Finally, we show that for a class of piecewise linear switched systems, the inertia of the system is not sufficient to determine its stability. A number of examples are provided to illustrate the concepts discussed in this paper. © 2012 South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.

引用

页码：176 / 183

页数：7

共 28 条

[21]

Aubin J.P., Frankowska H., Set-Valued Analysis, (1990)

[22]

Grunbaum B., Convex Polytopes, (2003)

[23]

Hartman P., Ordinary Differential Equations, (2002)

[24]

Palis Jr. J., de Melo W., Manning A.K., Geometric Theory of Dynamical Systems, (1982)

[25]

Cort'es J., Discontinuous dynamical systems: a tutorial on solutions, nonsmooth analysis, and stability, IEEE Control Systems Magazine, 28, 3, pp. 36-73, (2008)

[26]

Shorten R., Wirth F., Mason O., Et al., Stability criteria for switched and hybrid systems, SIAM Review, 49, 4, pp. 545-592, (2007)

[27]

Greub W.H., Linear Algebra, (1967)

[28]

Roman S., Advanced Linear Algebra, (2005)

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