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Stability and Stabilization of Discontinuous Systems and NonsmoothLyapunov Functions

Published online by Cambridge University Press:  15 August 2002

Andrea Bacciotti  and
Francesca Ceragioli
Andrea Bacciotti
Affiliation:
Dipartimento di Matematica del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy; bacciotti@polito.it.
Francesca Ceragioli
Affiliation:
Dipartimento di Matematica “U. Dini", Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy; ceragio@udini.math.unifi.it.
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Abstract

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 sufficient conditions for a system to be stabilized by means of a feedback law of the Jurdjevic-Quinn type.


Keywords

StabilitystabilizationClarke gradientLyapunov functionsLaSalle principle.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 361 - 376
Copyright
© EDP Sciences, SMAI, 1999

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