Connections between stability conditions for slowly time-varying and switched linear systems

Xiaobin Gao; Daniel Liberzon; Ji Liu; Tamer Basar

doi:10.1109/CDC.2015.7402555

Connections between stability conditions for slowly time-varying and switched linear systems

Xiaobin Gao, Daniel Liberzon, Ji Liu, Tamer Basar

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

Abstract

This paper establishes an explicit relationship between stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation of a matrix-valued function is introduced to characterize the variation of the system matrix. Using this concept, a result generalizing existing stability conditions for slowly time-varying linear systems is derived. As a special case of this result, it is shown that a switched linear system is globally exponentially stable if the average dwell time of the switching signal is large enough, which qualitatively matches known results in the literature.

Original language	English (US)
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2329-2334
Number of pages	6
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7402555
State	Published - Feb 8 2015
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015

Publication series

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

Other

Other	54th IEEE Conference on Decision and Control, CDC 2015
Country/Territory	Japan
City	Osaka
Period	12/15/15 → 12/18/15

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC.2015.7402555

Library availability

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Cite this

Gao, X., Liberzon, D., Liu, J., & Basar, T. (2015). Connections between stability conditions for slowly time-varying and switched linear systems. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 2329-2334). Article 7402555 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402555

Connections between stability conditions for slowly time-varying and switched linear systems. / Gao, Xiaobin; Liberzon, Daniel; Liu, Ji et al.
54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2329-2334 7402555 (Proceedings of the IEEE Conference on Decision and Control).

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

Gao, X, Liberzon, D, Liu, J & Basar, T 2015, Connections between stability conditions for slowly time-varying and switched linear systems. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7402555, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2329-2334, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7402555

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Connections between stability conditions for slowly time-varying and switched linear systems

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