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Hybrid Dynamical SystemsModeling, Stability, and Robustness$
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Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

Print publication date: 2012

Print ISBN-13: 9780691153896

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153896.001.0001

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Invariance principles

Invariance principles

(p.169) Chapter Eight Invariance principles
Hybrid Dynamical Systems

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Princeton University Press

This chapter discusses invariance principles, which characterize the sets to which precompact solutions to a dynamical system must converge. They rely on invariance properties of ω‎-limit sets of solutions, and additionally on Lyapunov-like functions, which do not increase along solutions, or output functions. Invariance principles which rely on Lyapunov-like functions are first presented, and their applications to the analysis of asymptotic stability are then described. The chapter next states an invariance principle involving not a Lyapunov-like function, but an output function having a certain property not along all solutions, but only along the solution whose behavior is being analyzed. Finally, the chapter presents invariance principles for switching systems with dwell-time switching signals modeled as hybrid systems.

Keywords:   invariance principles, precompact solutions, Lyapunov-like functions, asymptotic stability, output function, switching systems, ω‎-limit sets

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