On Topological Entropy of Switched Linear Systems with Diagonal, Triangular, and General Matrices

Guosong Yang, A. James Schmidt, Daniel Liberzon

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

Abstract

This paper introduces a notion of topological entropy for switched systems, formulated using the minimal number of initial states needed to approximate all initial states within a finite precision. We show that it can be equivalently defined using the maximal number of initial states separable within a finite precision, and introduce switching-related quantities such as the active time of each mode, which prove to be useful in calculating the topological entropy of switched linear systems. For general switched linear systems, we show that the topological entropy is independent of the set of initial states, and establish upper and lower bounds using the active-time-weighted averages of the norms and traces of system matrices in individual modes, respectively. For switched linear systems with scalar-valued state or simultaneously diagonalizable matrices, we derive formulae for the topological entropy using active-time-weighted averages of eigenvalues, which can be extended to the case with simultaneously triangularizable matrices to obtain an upper bound. In these three cases with special matrix structure, we also provide more general but more conservative upper bounds for the topological entropy.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5682-5687
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Fingerprint Dive into the research topics of 'On Topological Entropy of Switched Linear Systems with Diagonal, Triangular, and General Matrices'. Together they form a unique fingerprint.

  • Cite this

    Yang, G., James Schmidt, A., & Liberzon, D. (2019). On Topological Entropy of Switched Linear Systems with Diagonal, Triangular, and General Matrices. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 5682-5687). [8619087] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619087