Limit and Morse Sets for Deterministic Hybrid Systems

• Kimberly Ayers ^[1] ; Xavier Garcia ^[2] ; Jennifer Kunze ^[6] ; Thomas Rudelius ^[3] ; Anthony Sanchez ^[4] ; Sijing Shao ^[1] ; Emily Speranza ^[5]
  1. [1] Iowa State University

     Iowa State University

     Township of Franklin, Estados Unidos

     
  2. [2] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  3. [3] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     
  4. [4] Arizona State University

     Arizona State University

     Estados Unidos

     
  5. [5] Carroll College

     Carroll College

     Estados Unidos

     
  6. [6] Saint Mary’s College of Maryland (USA)

  Mostrar afiliaciones +
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 2, 2013, págs. 335-360
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The term “hybrid system” refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right formulation, a hybrid system can be treated as a dynamical system on a compact space. This allows us to study its limit sets. We examine the Morse decompositions of hybrid systems, find a sufficient condition for the existence of a non-trivial Morse decomposition, and study the Morse sets of such a decomposition.

    Finally, we consider the case in which the Markovian perturbations are small, showing that trajectories in a hybrid system with small perturbations behave similarly to those of the unperturbed dynamical system.