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Lyapunov Stability Theory of Nonsmooth Systems

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

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