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Zbl 1085.49008
Brogliato, Bernard; Goeleven, Daniel
The Krakovskii-LaSalle invariance principle for a class of unilateral dynamical systems. (English)
[J] Math. Control Signals Syst. 17, No. 1, 57-76 (2005). ISSN 0932-4194; ISSN 1435-568X/e

The main result of the paper consists in an extension of the Krakovskii-LaSalle invariance lemma to a class of nonsmooth dynamical systems involving evolution variational inequalities. There are given basic consequences of this important result regarding the stability theory. Applications are presented for linear and nonlinear evolution variational inequalities. The results are illustrated in studying the absolute stability and electric circuit problems.
[Dumitru Motreanu (Perpignan)]

MSC 2000:: *49J40 Variational methods including variational inequalities
49K40 Sensitivity of optimal solutions in the presence of perturbations
34D20 Lyapunov stability of ODE
34A60 ODE with multivalued right-hand sides
70F25 Nonholonomic systems
93D05 Lyapunov and other classical stabilities of control systems

Keywords: Lyapunov stability; unilateral constraints; LaSalle invariance principle; variational inequality

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