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On topological entropy and stability of switched linear systems

Authors:

João P. Hespanha,

Daniel LiberzonAuthors Info & Claims

HSCC '19: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

Pages 119 - 127

https://doi.org/10.1145/3302504.3311815

Published: 16 April 2019 Publication History

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.

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Cited By

Sibai HMitra S(2023)State Estimation of Continuous-Time Dynamical Systems With Uncertain Inputs With Bounded Variation: Entropy, Bit Rates, and Relation With Switched SystemsIEEE Transactions on Automatic Control10.1109/TAC.2023.325051068:12(7041-7056)Online publication date: Dec-2023
https://doi.org/10.1109/TAC.2023.3250510
Yang GLiberzon DHespanha J(2023)Topological entropy of switched nonlinear and interconnected systemsMathematics of Control, Signals, and Systems10.1007/s00498-023-00346-535:3(641-683)Online publication date: 2-Apr-2023
https://doi.org/10.1007/s00498-023-00346-5
Tomar MZamani M(2022)On a notion of entropy for reachability properties2022 American Control Conference (ACC)10.23919/ACC53348.2022.9867868(781-786)Online publication date: 8-Jun-2022
https://doi.org/10.23919/ACC53348.2022.9867868
Show More Cited By

Index Terms

On topological entropy and stability of switched linear systems
1. Computing methodologies
  1. Modeling and simulation

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cover image ACM Conferences

HSCC '19: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

April 2019

299 pages

ISBN:9781450362825

DOI:10.1145/3302504

Program Chairs:
Necmiye Ozay
University of Michigan
,
Pavithra Prabhakar
Kansas State University

Copyright © 2019 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 16 April 2019

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HSCC '19: 22nd ACM International Conference on Hybrid Systems: Computation and Control

April 16 - 18, 2019

Quebec, Montreal, Canada

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Cited By

Sibai HMitra S(2023)State Estimation of Continuous-Time Dynamical Systems With Uncertain Inputs With Bounded Variation: Entropy, Bit Rates, and Relation With Switched SystemsIEEE Transactions on Automatic Control10.1109/TAC.2023.325051068:12(7041-7056)Online publication date: Dec-2023
https://doi.org/10.1109/TAC.2023.3250510
Yang GLiberzon DHespanha J(2023)Topological entropy of switched nonlinear and interconnected systemsMathematics of Control, Signals, and Systems10.1007/s00498-023-00346-535:3(641-683)Online publication date: 2-Apr-2023
https://doi.org/10.1007/s00498-023-00346-5
Tomar MZamani M(2022)On a notion of entropy for reachability properties2022 American Control Conference (ACC)10.23919/ACC53348.2022.9867868(781-786)Online publication date: 8-Jun-2022
https://doi.org/10.23919/ACC53348.2022.9867868
Berger GJungers R(2022)Worst-case topological entropy and minimal data rate for state estimation of switched linear systemsCommunications of the ACM10.1145/350526965:2(111-118)Online publication date: 24-Jan-2022
https://dl.acm.org/doi/10.1145/3505269
Vicinansa GLiberzon DBogomolov SJungers R(2021)Quantizer design for switched linear systems with minimal data-rateProceedings of the 24th International Conference on Hybrid Systems: Computation and Control10.1145/3447928.3456645(1-11)Online publication date: 19-May-2021
https://dl.acm.org/doi/10.1145/3447928.3456645
Yang GLiberzon DHespanha JBogomolov SJungers R(2021)Topological entropy of switched nonlinear systemsProceedings of the 24th International Conference on Hybrid Systems: Computation and Control10.1145/3447928.3456642(1-11)Online publication date: 19-May-2021
https://dl.acm.org/doi/10.1145/3447928.3456642
Berger GJungers RAmes ASeshia SDeshmukh J(2020)Worst-case topological entropy and minimal data rate for state observation of switched linear systemsProceedings of the 23rd International Conference on Hybrid Systems: Computation and Control10.1145/3365365.3382195(1-11)Online publication date: 22-Apr-2020
https://dl.acm.org/doi/10.1145/3365365.3382195
Yang GSchmidt ALiberzon DHespanha J(2020)Topological entropy of switched linear systems: general matrices and matrices with commutation relationsMathematics of Control, Signals, and Systems10.1007/s00498-020-00265-932:3(411-453)Online publication date: 9-Sep-2020
https://doi.org/10.1007/s00498-020-00265-9

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