Further results on strict Lyapunov functions for rapidly time-varying nonlinear systems

Frédéric F. Mazenc (1, 2) , Michael Malisoff (3) , Marcio de Queiroz (4)

1 ASB - Analyse des Systèmes et Biométrie
2 MERE - Water Resource Modeling
3 Department of mathematics
4 LSU - Louisiana State University

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform global asymptotic, and input-to-state stability of fast time-varying dynamics. We also construct strict Lyapunov functions for our systems using a strictification approach. We illustrate our results using several examples.

Mots clés: TIME-VARYING SYSTEMS; INPUT-TO-STATE STABILITY; LYAPUNOV FUNCTION CONSTRUCTIONS

Mots clés: SYSTEME DE CONTROLE NON LINEAIRE; FONCTION LYAPUNOV STRICTE; COMMANDE INSTATIONNAIRE; STABILITE

Domaines: Automatique

Frédéric F. Mazenc, Michael Malisoff, Marcio de Queiroz. Further results on strict Lyapunov functions for rapidly time-varying nonlinear systems. Automatica, 2006, 42 (10), pp.1663-1671. ⟨10.1016/j.automatica.2006.05.020⟩. ⟨hal-02657650⟩