Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions
نویسندگان
چکیده
منابع مشابه
Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions
We study stability and stabilizability properties of systems with discontinuous righthand side (with solutions intended in Filippov’s sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine with respect to the input: we give some...
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Differential equations with discontinuous righthand side and solutions intended in Carathéodory sense are considered. For these equations sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.
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The main result of this note is an external stabilizability theorem for discontinuous systems affine in the control (with solutions intended in the Filippov’s sense). In order to get it we first prove a sufficient condition for external stability which makes use of nonsmooth Lyapunov-like functions.
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It is shown that the existence of a continuous controlLyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finitedimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative that has been studied in set-valued analysis and the theory of differential inclusions with various names such as “upper conting...
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ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 1999
ISSN: 1292-8119,1262-3377
DOI: 10.1051/cocv:1999113