Average Dwell-Time Bounds for ISS and Integral ISS of Switched Systems using Lyapunov Functions

Shenyu Liu; Aneel Tanwani; Daniel Liberzon

doi:10.1109/CDC42340.2020.9304445

Average Dwell-Time Bounds for ISS and Integral ISS of Switched Systems using Lyapunov Functions

Shenyu Liu, Aneel Tanwani, Daniel Liberzon

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

Abstract

The problem of input-to-state stability (ISS), and its integral version (iISS), is considered for switched systems with inputs and resets. The individual subsystems are assumed to be ISS (resp. iISS) with nonlinear decay rates in dissipation inequalities associated with the Lyapunov function of each subsystem. The change in the value of Lyapunov functions at switching instants is described by a nonlinear growth function. A generalized lower bound is computed for average dwell-time (ADT) to guarantee ISS/iISS of the switched system. In particular, an explicit formula of ADT lower bound is given for switched bilinear systems with zero-input-stable subsystems.

Original language	English (US)
Title of host publication	2020 59th IEEE Conference on Decision and Control, CDC 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6291-6296
Number of pages	6
ISBN (Electronic)	9781728174471
DOIs	https://doi.org/10.1109/CDC42340.2020.9304445
State	Published - Dec 14 2020
Event	59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of Duration: Dec 14 2020 → Dec 18 2020

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2020-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	59th IEEE Conference on Decision and Control, CDC 2020
Country/Territory	Korea, Republic of
City	Virtual, Jeju Island
Period	12/14/20 → 12/18/20

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC42340.2020.9304445

Library availability

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Cite this

Liu, S., Tanwani, A., & Liberzon, D. (2020). Average Dwell-Time Bounds for ISS and Integral ISS of Switched Systems using Lyapunov Functions. In 2020 59th IEEE Conference on Decision and Control, CDC 2020 (pp. 6291-6296). Article 9304445 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC42340.2020.9304445

Average Dwell-Time Bounds for ISS and Integral ISS of Switched Systems using Lyapunov Functions. / Liu, Shenyu; Tanwani, Aneel; Liberzon, Daniel.
2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. p. 6291-6296 9304445 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December).

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

Liu, S, Tanwani, A & Liberzon, D 2020, Average Dwell-Time Bounds for ISS and Integral ISS of Switched Systems using Lyapunov Functions. in 2020 59th IEEE Conference on Decision and Control, CDC 2020., 9304445, Proceedings of the IEEE Conference on Decision and Control, vol. 2020-December, Institute of Electrical and Electronics Engineers Inc., pp. 6291-6296, 59th IEEE Conference on Decision and Control, CDC 2020, Virtual, Jeju Island, Korea, Republic of, 12/14/20. https://doi.org/10.1109/CDC42340.2020.9304445

Liu S, Tanwani A, Liberzon D. Average Dwell-Time Bounds for ISS and Integral ISS of Switched Systems using Lyapunov Functions. In 2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc. 2020. p. 6291-6296. 9304445. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC42340.2020.9304445

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abstract = "The problem of input-to-state stability (ISS), and its integral version (iISS), is considered for switched systems with inputs and resets. The individual subsystems are assumed to be ISS (resp. iISS) with nonlinear decay rates in dissipation inequalities associated with the Lyapunov function of each subsystem. The change in the value of Lyapunov functions at switching instants is described by a nonlinear growth function. A generalized lower bound is computed for average dwell-time (ADT) to guarantee ISS/iISS of the switched system. In particular, an explicit formula of ADT lower bound is given for switched bilinear systems with zero-input-stable subsystems.",

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N2 - The problem of input-to-state stability (ISS), and its integral version (iISS), is considered for switched systems with inputs and resets. The individual subsystems are assumed to be ISS (resp. iISS) with nonlinear decay rates in dissipation inequalities associated with the Lyapunov function of each subsystem. The change in the value of Lyapunov functions at switching instants is described by a nonlinear growth function. A generalized lower bound is computed for average dwell-time (ADT) to guarantee ISS/iISS of the switched system. In particular, an explicit formula of ADT lower bound is given for switched bilinear systems with zero-input-stable subsystems.

AB - The problem of input-to-state stability (ISS), and its integral version (iISS), is considered for switched systems with inputs and resets. The individual subsystems are assumed to be ISS (resp. iISS) with nonlinear decay rates in dissipation inequalities associated with the Lyapunov function of each subsystem. The change in the value of Lyapunov functions at switching instants is described by a nonlinear growth function. A generalized lower bound is computed for average dwell-time (ADT) to guarantee ISS/iISS of the switched system. In particular, an explicit formula of ADT lower bound is given for switched bilinear systems with zero-input-stable subsystems.

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Average Dwell-Time Bounds for ISS and Integral ISS of Switched Systems using Lyapunov Functions

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