On topological entropy and stability of switched linear systems

Guosong Yang, João P. Hespanha, Daniel Liberzon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper studies topological entropy and stability properties of switched linear systems. First, we show that the exponential growth rates of solutions of a switched linear system are essentially upper bounded by its topological entropy. Second, we estimate the topological entropy of a switched linear system by decomposing it into a part that is generated by scalar multiples of the identity matrix and a part that has zero entropy, and proving that the overall topological entropy is upper bounded by that of the former. Third, we prove that a switched linear system is globally exponentially stable if its topological entropy remains zero under a destabilizing perturbation. Finally, the entropy estimation via decomposition and the entropy-based stability condition are applied to three classes of switched linear systems to construct novel upper bounds for topological entropy and novel sufficient conditions for global exponential stability.

Original languageEnglish (US)
Title of host publicationHSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems
Subtitle of host publicationComputation and Control
PublisherAssociation for Computing Machinery, Inc
Pages119-127
Number of pages9
ISBN (Electronic)9781450362825
DOIs
StatePublished - Apr 16 2019
Event22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019 - Montreal, Canada
Duration: Apr 16 2019Apr 18 2019

Publication series

NameHSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control

Conference

Conference22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019
CountryCanada
CityMontreal
Period4/16/194/18/19

Keywords

  • Stability
  • Switched systems
  • Topological entropy

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Networks and Communications
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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