Lyapunov Stability Theory of Nonsmooth Systems

Daniel Shevitz (1) , Brad Paden (1)

1 Department of Mechanical Engineering [Santa Barbara]

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 trajec· tories. Computable tests based on Filipov's differential inclusion and Clarke's generalized gradient 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.

Mots clés: differential equations; Lyapunov methods; stability; nonsmooth systems; invariance principle; nonsmooth Lipschitz continuous Lyapunov functions

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Vibrations [physics.class-ph]; Génie mécanique [physics.class-ph]; Dynamique, vibrations; Structures

Daniel Shevitz, Brad Paden. Lyapunov Stability Theory of Nonsmooth Systems. IEEE Transactions on Automatic Control, 1994, 39 (9), pp.1910-1914. ⟨10.1109/9.317122⟩. ⟨hal-01634266⟩