Lyapunov stability theory of nonsmooth systems

Author

Shevitz, Daniel ; Paden, Brad

Author_Institution

Dept. of Mech. Eng., California Univ., Santa Barbara, CA, USA

fYear

1993

fDate

15-17 Dec 1993

Firstpage

416

Abstract

This paper develops nonsmooth Lyapunov stability theory and LaSalle´s invariance principle for a class of nonsmooth Lipschitz continuous Lyapunov functions and absolutely continuous state trajectories. Computable tests based on Filippov´s differential inclusion and Clarke´s generalized gradient (1983) are derived. The primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

Keywords

Lyapunov methods; differential equations; stability; Lyapunov stability theory; VSS; absolutely continuous state trajectories; differential equation equilibrium stability; differential inclusion; discontinuous right hand side; generalized gradient; invariance principle; nonsmooth Lipschitz continuous Lyapunov functions; nonsmooth dynamic systems; nonsmooth systems; variable structure control; Area measurement; Books; Control systems; Differential equations; Lyapunov method; Mechanical engineering; Stability analysis; System testing; Time measurement; Variable structure systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1993., Proceedings of the 32nd IEEE Conference on

Conference_Location

San Antonio, TX

Print_ISBN

0-7803-1298-8

Type

conf

DOI

10.1109/CDC.1993.325114

Filename

325114