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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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Uniform asymptotic stability, an initial treatment

Uniform asymptotic stability, an initial treatment

(p.43) Chapter Three Uniform asymptotic stability, an initial treatment
Hybrid Dynamical Systems

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Princeton University Press

This chapter focuses on the uniform asymptotic stability of a closed set. Asymptotic stability is a fundamental property of dynamical systems—one that is usually desired in natural and engineered systems. It provides qualitative information about solutions, especially a characterization of the solutions' long-term trends. The asymptotic stability of a closed set, rather than of an equilibrium point, is significant since the solutions of a hybrid system often do not settle down to an equilibrium point. Furthermore, the asymptotic stability of an equilibrium point is a special case of asymptotic stability of a closed set. Namely, an equilibrium point is a closed set containing a single point.

Keywords:   uniform asymptotic stability, closed sets, equilibrium points, pre-asymptotic stability, Lyapunov functions, Lyapunov conditions, dynamical systems

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