Mixed H2 / H∞ control of uncertain jumping time-delay systems

Magdi S. Mahmoud; Fouad M. AL-Sunni; Yan Shi

doi:10.1016/j.jfranklin.2008.03.001

Mixed H₂ / H_∞ control of uncertain jumping time-delay systems

Magdi S. Mahmoud^*
, Fouad M. AL-Sunni
, Yan Shi

^*Corresponding author for this work

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

24 Scopus citations

Abstract

In this paper, we investigate a class of linear continuous-time systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state with time-varying and bounded delays. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Employing norm-bounded parametric uncertainties and utilizing the second-method of Lyapunov, we examine the problem of designing a mixed H₂ / H_∞ controller which minimizes a quadratic H₂ performance measure while satisfying a prescribed H_∞-norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the mixed H₂ / H_∞ controller and the associated performance upper bound could be cast in the form of linear matrix inequalities.

Original language	English
Pages (from-to)	536-552
Number of pages	17
Journal	Journal of the Franklin Institute
Volume	345
Issue number	5
DOIs	https://doi.org/10.1016/j.jfranklin.2008.03.001
State	Published - Aug 2008

Bibliographical note

Funding Information:
The authors would like to thank the anonymous reviewers for many constructive comments which helped to improve the final draft of the paper. The general support of KFUPM to undertake this research work is acknowledged.

Keywords

Asymptotic stability
Mixed H / H control
Norm-bounded parametric uncertainties
State-delay systems

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

Access to Document

10.1016/j.jfranklin.2008.03.001

Cite this

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title = "Mixed H2 / H∞ control of uncertain jumping time-delay systems",

abstract = "In this paper, we investigate a class of linear continuous-time systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state with time-varying and bounded delays. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Employing norm-bounded parametric uncertainties and utilizing the second-method of Lyapunov, we examine the problem of designing a mixed H2 / H∞ controller which minimizes a quadratic H2 performance measure while satisfying a prescribed H∞-norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the mixed H2 / H∞ controller and the associated performance upper bound could be cast in the form of linear matrix inequalities.",

keywords = "Asymptotic stability, Mixed H / H control, Norm-bounded parametric uncertainties, State-delay systems",

author = "Mahmoud, \{Magdi S.\} and AL-Sunni, \{Fouad M.\} and Yan Shi",

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AU - Mahmoud, Magdi S.

AU - AL-Sunni, Fouad M.

AU - Shi, Yan

N1 - Funding Information: The authors would like to thank the anonymous reviewers for many constructive comments which helped to improve the final draft of the paper. The general support of KFUPM to undertake this research work is acknowledged.

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N2 - In this paper, we investigate a class of linear continuous-time systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state with time-varying and bounded delays. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Employing norm-bounded parametric uncertainties and utilizing the second-method of Lyapunov, we examine the problem of designing a mixed H2 / H∞ controller which minimizes a quadratic H2 performance measure while satisfying a prescribed H∞-norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the mixed H2 / H∞ controller and the associated performance upper bound could be cast in the form of linear matrix inequalities.

AB - In this paper, we investigate a class of linear continuous-time systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state with time-varying and bounded delays. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Employing norm-bounded parametric uncertainties and utilizing the second-method of Lyapunov, we examine the problem of designing a mixed H2 / H∞ controller which minimizes a quadratic H2 performance measure while satisfying a prescribed H∞-norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the mixed H2 / H∞ controller and the associated performance upper bound could be cast in the form of linear matrix inequalities.

KW - Asymptotic stability

KW - Mixed H / H control

KW - Norm-bounded parametric uncertainties

KW - State-delay systems

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