Topological entropy of switched nonlinear systems

Guosong Yang, Daniel Liberzon, João P. Hespanha

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

Abstract

This paper studies topological entropy of switched nonlinear systems. We construct a general upper bound for the topological entropy in terms of an average of the asymptotic suprema of the measures of Jacobian matrices of individual modes, weighted by the corresponding active rates. A general lower bound is constructed in terms of an active-rate-weighted average of the asymptotic infima of the traces of these Jacobian matrices. For switched systems with diagonal modes, we construct upper and lower bounds that only depend on the eigenvalues of Jacobian matrices, their relative order among individual modes, and the active rates. For both cases, we also construct more conservative upper bounds that require less information on the switching, with their relations illustrated by numerical examples of a switched Lotka-Volterra ecosystem model.

Original languageEnglish (US)
Title of host publicationHSCC 2021 - Proceedings of the 24th International Conference on Hybrid Systems
Subtitle of host publicationComputation and Control (part of CPS-IoT Week)
PublisherAssociation for Computing Machinery, Inc
ISBN (Electronic)9781450383394
DOIs
StatePublished - May 19 2021
Event24th ACM International Conference on Hybrid Systems Computation and Control, HSCC 2021, held as part of the 14th Cyber Physical Systems and Internet-of-Things Week, CPS-IoT Week 2021 - Virtual, Online, United States
Duration: May 19 2021May 21 2021

Publication series

NameHSCC 2021 - Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control (part of CPS-IoT Week)

Conference

Conference24th ACM International Conference on Hybrid Systems Computation and Control, HSCC 2021, held as part of the 14th Cyber Physical Systems and Internet-of-Things Week, CPS-IoT Week 2021
Country/TerritoryUnited States
CityVirtual, Online
Period5/19/215/21/21

Keywords

  • nonlinear systems
  • switched systems
  • topological entropy

ASJC Scopus subject areas

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

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