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

In: Splitting Algorithms, Modern Operator Theory, and Applications

Author

Listed:
  • Rafal Goebel

    (Loyola University Chicago, Department of Mathematics and Statistics)

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.

Suggested Citation

  • Rafal Goebel, 2019. "A Glimpse at Pointwise Asymptotic Stability for Continuous-Time and Discrete-Time Dynamics," Springer Books, in: Heinz H. Bauschke & Regina S. Burachik & D. Russell Luke (ed.), Splitting Algorithms, Modern Operator Theory, and Applications, chapter 0, pages 243-267, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-25939-6_10
    DOI: 10.1007/978-3-030-25939-6_10
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