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Stabilization of Linear Switched Delay Systems: ℋ2 and ℋ∞ Methods

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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 information

Authors and Affiliations

  1. Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 985, Dhahran, 31261, Saudi Arabia

    M. S. Mahmoud

  2. Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd, CF 37 1DL, UK

    P. Shi

  3. ILSCM, School of Science and Engineering, Victoria University, Melbourne, Australia

    P. Shi

  4. School of Mathematics and Statistics, University of South Australia, Adelaide, Australia

    P. Shi

  5. Systems Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 1626, Dhahran, 31261, Saudi Arabia

    A. W. A. Saif

Authors
  1. M. S. Mahmoud
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  2. P. Shi
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  3. A. W. A. Saif
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Correspondence to M. S. Mahmoud.

Additional information

Communicated by F.E. Udwadia.

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Mahmoud, M.S., Shi, P. & Saif, A.W.A. Stabilization of Linear Switched Delay Systems: ℋ2 and ℋ∞ Methods. J Optim Theory Appl 142, 583–601 (2009). https://doi.org/10.1007/s10957-009-9527-2

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  • DOI: https://doi.org/10.1007/s10957-009-9527-2

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