A Glimpse at Pointwise Asymptotic Stability for Continuous-Time and Discrete-Time Dynamics

Rafal Goebel ()
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Rafal Goebel: Loyola University Chicago, Department of Mathematics and Statistics

Chapter Chapter 10 in Splitting Algorithms, Modern Operator Theory, and Applications, 2019, pp 243-267 from Springer

Abstract: Abstract Given a dynamical system, pointwise asymptotic stability, also called semistability, of a set requires that every point in the set be a Lyapunov stable equilibrium, and that every solution converge to one of the equilibria in the set. This note provides examples of pointwise asymptotic stability related to optimization and states select results from the literature, focusing on necessary and sufficient Lyapunov and Lyapunov-like conditions for and robustness of this stability property. Background on the classical asymptotic stability is included.

Keywords: Pointwise asymptotic stability; Differential inclusion; Difference inclusion; Monotone operator; Set-valued Lyapunov function; 93D05; 49J53; 90C25; 34D20; 47H05 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-25939-6_10

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DOI: 10.1007/978-3-030-25939-6_10

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