Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems

Shenyu Liu; Daniel Liberzon

doi:10.1109/CDC.2018.8619364

Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems

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

Abstract

In this paper we study several stability properties for state-dependent switched systems. We examine the gap between global asymptotic stability and uniform global asymptotic stability, and illustrate it with an example. Several regularity assumptions are proposed in order to obtain the equivalence between these two stability properties. Based on this equivalence, we are able to show that global stability and asymptotic gain imply input-to-state stability for state-dependent switched systems, which is the main result of the paper. The proof consists of a bypass via an auxiliary system which takes in a bounded disturbance, and showing that this system is uniformly globally asymptotically stable.

Original language	English (US)
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2360-2365
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619364
State	Published - Jan 18 2019
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country	United States
City	Miami
Period	12/17/18 → 12/19/18

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2018.8619364

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Liu, S., & Liberzon, D. (2019). Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 2360-2365). [8619364] (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.2018.8619364

Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems. / Liu, Shenyu; Liberzon, Daniel.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2360-2365 8619364 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

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

Liu, S & Liberzon, D 2019, Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619364, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 2360-2365, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619364

Liu S, Liberzon D. Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2360-2365. 8619364. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619364

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abstract = "In this paper we study several stability properties for state-dependent switched systems. We examine the gap between global asymptotic stability and uniform global asymptotic stability, and illustrate it with an example. Several regularity assumptions are proposed in order to obtain the equivalence between these two stability properties. Based on this equivalence, we are able to show that global stability and asymptotic gain imply input-to-state stability for state-dependent switched systems, which is the main result of the paper. The proof consists of a bypass via an auxiliary system which takes in a bounded disturbance, and showing that this system is uniformly globally asymptotically stable.",

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AB - In this paper we study several stability properties for state-dependent switched systems. We examine the gap between global asymptotic stability and uniform global asymptotic stability, and illustrate it with an example. Several regularity assumptions are proposed in order to obtain the equivalence between these two stability properties. Based on this equivalence, we are able to show that global stability and asymptotic gain imply input-to-state stability for state-dependent switched systems, which is the main result of the paper. The proof consists of a bypass via an auxiliary system which takes in a bounded disturbance, and showing that this system is uniformly globally asymptotically stable.

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