Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems

Details Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems

2006-10-06

arxiv.org/abs/math/0610210v1

Nonlinear Analysis Hybrid Systems, published online February 20, 2007

Mathematics

Optimization and Control

14 pages. Accepted for publication in Nonlinear Analysis: Hybrid Systems and Applications on September 6, 2006

Scientific paper

10.1016/j.nahs.2006.12.005

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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