Further remarks on strict input-to-state stable Lyapunov functions for time-varying systems |
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| Authors: | Michael Malisoff [Author Vitae] |
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| Affiliation: | a Department of Mathematics, 304 Lockett Hall, Louisiana State University, Baton Rouge, LA 70803-4918, USA
b Projet MERE INRIA-INRA, UMR Analyse des Systèmes et Biométrie INRA, 2, pl. Viala, 34060 Montpellier, France |
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| Abstract: | We study the stability properties of a class of time-varying non-linear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our given Lyapunov functions which guarantee the existence of strict ISS Lyapunov functions for our systems. Next, we provide simple direct constructions of explicit strict ISS Lyapunov functions for our systems by applying an integral smoothing method. We illustrate our constructions using a tracking problem for a rotating rigid body. |
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| Keywords: | Lyapunov functions Input-to-state stabilization Non-autonomous systems |
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