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

Authors:
FréDéRic Mazenc;Michael Malisoff;Marcio S. De Queiroz
Affiliations:
Projet MERE INRIA-INRA, UMR Analyse des Systèmes et Biométrie INRA, 2 pl. Viala, 34060 Montpellier, France;Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, USA;Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803-6413, USA
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

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.