Multiple Lyapunov functions and other analysis tools for switched and hybrid systems

Author

Branicky, Michael S.

Author_Institution

Dept. of Electr. Eng. & Appl. Phys., Case Western Reserve Univ., Cleveland, OH, USA

Volume

43

Issue

4

fYear

1998

fDate

4/1/1998 12:00:00 AM

Firstpage

475

Lastpage

482

Abstract

We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson´s theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of “continuous switched” systems

Keywords

Lyapunov methods; continuous time systems; control system analysis; limit cycles; nonlinear systems; stability; variable structure systems; Bendixson theorem; Lagrange stability; Lipschitz continuous vector; Lyapunov functions; hybrid systems; iterated function systems; limit cycle; nonlinear systems; stability analysis; switched systems; variable structure systems; Automata; Control systems; Difference equations; Differential equations; Lagrangian functions; Limit-cycles; Lyapunov method; Stability analysis; Switched systems; Switches;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.664150

Filename

664150