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

Authors
Journal
Nonlinear Analysis Hybrid Systems
1751-570X
Publisher
Elsevier
Publication Date
Volume
2
Issue
2
Identifiers
DOI: 10.1016/j.nahs.2006.12.005
Keywords
  • Strict Lyapunov Functions
  • Discrete And Hybrid Time-Varying Systems

Abstract

Abstract 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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