Stabilization of linear switched delay systems: H2 and H∞ methods

M. S. Mahmoud; P. Shi; A. W.A. Saif

doi:10.1007/s10957-009-9527-2

Stabilization of linear switched delay systems: H₂ and H_∞ methods

M. S. Mahmoud, P. Shi, A. W.A. Saif

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

This paper presents new results pertaining to the delay-dependent stability and control synthesis of a class of linear switched continuous-time systems with time-varying delays. A new state transformation is introduced to exhibit the delay-dependent dynamics in the slow-time scale. For stability, we construct an appropriate selective Lyapunov functional to derive delay-dependent LMI-based sufficient conditions under arbitrary switching and without relying to overbounding. For the control synthesis, we design switched feedback schemes based on quadratic H₂, H_∞ and simultaneous H₂/H_∞ performance criteria. Under the developed transformation, it is established that both the instantaneous and delayed feedback control yield identical results. Numerical examples are presented to illustrate the analytical development.

Original language	English
Pages (from-to)	583-601
Number of pages	19
Journal	Journal of Optimization Theory and Applications
Volume	142
Issue number	3
DOIs	https://doi.org/10.1007/s10957-009-9527-2
State	Published - Aug 2009

Bibliographical note

Funding Information:
Acknowledgement This work is partially supported by KFUPM research project No. IN080404, and Engineering and Physical Sciences Research Council, UK, EP/F029195.

Keywords

Delay-dependent stability
LMIs
Simultaneous H/H synthesis
Switched Lyapunov functional
Switched state-feedback
Switched time-delay systems

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Access to Document

10.1007/s10957-009-9527-2

Cite this

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title = "Stabilization of linear switched delay systems: H2 and H∞ methods",

abstract = "This paper presents new results pertaining to the delay-dependent stability and control synthesis of a class of linear switched continuous-time systems with time-varying delays. A new state transformation is introduced to exhibit the delay-dependent dynamics in the slow-time scale. For stability, we construct an appropriate selective Lyapunov functional to derive delay-dependent LMI-based sufficient conditions under arbitrary switching and without relying to overbounding. For the control synthesis, we design switched feedback schemes based on quadratic H2, H∞ and simultaneous H2/H∞ performance criteria. Under the developed transformation, it is established that both the instantaneous and delayed feedback control yield identical results. Numerical examples are presented to illustrate the analytical development.",

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author = "Mahmoud, \{M. S.\} and P. Shi and Saif, \{A. W.A.\}",

note = "Funding Information: Acknowledgement This work is partially supported by KFUPM research project No. IN080404, and Engineering and Physical Sciences Research Council, UK, EP/F029195.",

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AU - Shi, P.

AU - Saif, A. W.A.

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AB - This paper presents new results pertaining to the delay-dependent stability and control synthesis of a class of linear switched continuous-time systems with time-varying delays. A new state transformation is introduced to exhibit the delay-dependent dynamics in the slow-time scale. For stability, we construct an appropriate selective Lyapunov functional to derive delay-dependent LMI-based sufficient conditions under arbitrary switching and without relying to overbounding. For the control synthesis, we design switched feedback schemes based on quadratic H2, H∞ and simultaneous H2/H∞ performance criteria. Under the developed transformation, it is established that both the instantaneous and delayed feedback control yield identical results. Numerical examples are presented to illustrate the analytical development.

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KW - LMIs

KW - Simultaneous H/H synthesis

KW - Switched Lyapunov functional

KW - Switched state-feedback

KW - Switched time-delay systems

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