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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

Chapter:
(p.169) Chapter Eight Invariance principles
Source:
Hybrid Dynamical Systems
Author(s):

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153896.003.0008

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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