Robust stability and l2-gain analysis of linear discrete-time switched systems with dwell time

L. Allerhand; E. Gershon; U. Shaked

doi:10.3182/20120620-3-DK-2025.00094

Robust stability and l₂-gain analysis of linear discrete-time switched systems with dwell time

L. Allerhand^*, E. Gershon, U. Shaked

^*Corresponding author for this work

School of Electrical Engineering

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

Abstract

Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l2-gain analysis where a bounded real lemma is derived.

Original language	English
Title of host publication	ROCOND'12 - 7th IFAC Symposium on Robust Control Design
Publisher	IFAC Secretariat
Pages	588-592
Number of pages	5
Edition	13 PART 1
ISBN (Print)	9783902823038
DOIs	https://doi.org/10.3182/20120620-3-DK-2025.00094
State	Published - 2012
Event	7th IFAC Symposium on Robust Control Design, ROCOND'12 - Aalborg, Denmark Duration: 20 Jun 2012 → 22 Jun 2012

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Number	13 PART 1
Volume	45
ISSN (Print)	1474-6670

Conference

Conference	7th IFAC Symposium on Robust Control Design, ROCOND'12
Country/Territory	Denmark
City	Aalborg
Period	20/06/12 → 22/06/12

Access to Document

10.3182/20120620-3-DK-2025.00094

Cite this

Allerhand, L., Gershon, E., & Shaked, U. (2012). Robust stability and l₂-gain analysis of linear discrete-time switched systems with dwell time. In ROCOND'12 - 7th IFAC Symposium on Robust Control Design (13 PART 1 ed., pp. 588-592). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 45, No. 13 PART 1). IFAC Secretariat. https://doi.org/10.3182/20120620-3-DK-2025.00094

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abstract = "Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l2-gain analysis where a bounded real lemma is derived.",

author = "L. Allerhand and E. Gershon and U. Shaked",

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doi = "10.3182/20120620-3-DK-2025.00094",

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Allerhand, L, Gershon, E & Shaked, U 2012, Robust stability and l₂-gain analysis of linear discrete-time switched systems with dwell time. in ROCOND'12 - 7th IFAC Symposium on Robust Control Design. 13 PART 1 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. 13 PART 1, vol. 45, IFAC Secretariat, pp. 588-592, 7th IFAC Symposium on Robust Control Design, ROCOND'12, Aalborg, Denmark, 20/06/12. https://doi.org/10.3182/20120620-3-DK-2025.00094

Robust stability and l₂-gain analysis of linear discrete-time switched systems with dwell time. / Allerhand, L.; Gershon, E.; Shaked, U.
ROCOND'12 - 7th IFAC Symposium on Robust Control Design. 13 PART 1. ed. IFAC Secretariat, 2012. p. 588-592 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 45, No. 13 PART 1).

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

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