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Constructions of strict Lyapunov functions for discrete time and hybrid time-varying systems

✍ Scribed by Michael Malisoff; Frédéric Mazenc

Publisher
Elsevier
Year
2008
Tongue
English
Weight
352 KB
Volume
2
Category
Article
ISSN
1751-570X

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✦ Synopsis

We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct explicit strict Lyapunov functions for systems satisfying nonstrict discrete time analogs of the conditions from Matrosov's Theorem. We use our methods to build strict Lyapunov functions for time-varying hybrid systems that contain mixtures of continuous and discrete time evolutions.

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