IEEE Transactions on Automatic Control · 1994 · 1K citations · 6 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsSystem DynamicsContinuous Dynamical SystemsContinuous SystemsControl Of Dynamical SystemsControl TheoryDifferential SystemsStability TheoryControl Of Differential SystemsLyapunov FunctionsLyapunov StabilityLyapunov Stability AnalysisLyapunov Stability TheoryNonlinear StabilityStability Of Continuous SystemsSystem Stability
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 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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