Title :
Lyapunov stability theory of nonsmooth systems
Author :
Shevitz, Daniel ; Paden, Brad
Author_Institution :
Dept. of Mech. Eng., California Univ., Santa Barbara, CA, USA
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;
Conference_Titel :
Decision and Control, 1993., Proceedings of the 32nd IEEE Conference on
Conference_Location :
San Antonio, TX
Print_ISBN :
0-7803-1298-8
DOI :
10.1109/CDC.1993.325114
