On topological entropy and stability of switched linear systems

Guosong Yang; João P. Hespanha; Daniel Liberzon

doi:10.1145/3302504.3311815

On topological entropy and stability of switched linear systems

Guosong Yang, João P. Hespanha, Daniel Liberzon

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems
Subtitle of host publication	Computation and Control
Publisher	Association for Computing Machinery, Inc
Pages	119-127
Number of pages	9
ISBN (Electronic)	9781450362825
DOIs	https://doi.org/10.1145/3302504.3311815
State	Published - Apr 16 2019
Event	22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019 - Montreal, Canada Duration: Apr 16 2019 → Apr 18 2019

Publication series

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

Conference

Conference	22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019
Country	Canada
City	Montreal
Period	4/16/19 → 4/18/19

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

Access to Document

10.1145/3302504.3311815

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Cite this

Yang, G., Hespanha, J. P., & Liberzon, D. (2019). On topological entropy and stability of switched linear systems. In HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control (pp. 119-127). (HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control). Association for Computing Machinery, Inc. https://doi.org/10.1145/3302504.3311815

On topological entropy and stability of switched linear systems. / Yang, Guosong; Hespanha, João P.; Liberzon, Daniel.

HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control. Association for Computing Machinery, Inc, 2019. p. 119-127 (HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yang, G, Hespanha, JP & Liberzon, D 2019, On topological entropy and stability of switched linear systems. in HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control. HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control, Association for Computing Machinery, Inc, pp. 119-127, 22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019, Montreal, Canada, 4/16/19. https://doi.org/10.1145/3302504.3311815

Yang G, Hespanha JP, Liberzon D. On topological entropy and stability of switched linear systems. In HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control. Association for Computing Machinery, Inc. 2019. p. 119-127. (HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control). https://doi.org/10.1145/3302504.3311815

Yang, Guosong ; Hespanha, João P. ; Liberzon, Daniel. / On topological entropy and stability of switched linear systems. HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control. Association for Computing Machinery, Inc, 2019. pp. 119-127 (HSCC 2019 - Proceedings of the 2019 22nd ACM International Conference on Hybrid Systems: Computation and Control).

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N2 - 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.

AB - 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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