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Finite-time stability with respect to a closed invariant set for a class of discontinuous systems. (English) Zbl 1179.93142
Summary: This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of Filippov’s solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C10 Nonlinear systems in control theory
93D99 Stability of control systems
93C15 Control/observation systems governed by ordinary differential equations
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