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

M. S. Mahmoud (), P. Shi () and A. W. A. Saif ()
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M. S. Mahmoud: King Fahd University of Petroleum and Minerals
P. Shi: University of Glamorgan
A. W. A. Saif: King Fahd University of Petroleum and Minerals

Journal of Optimization Theory and Applications, 2009, vol. 142, issue 3, No 9, 583-601

Abstract: 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.

Keywords: Switched time-delay systems; Delay-dependent stability; Switched Lyapunov functional; Switched state-feedback; LMIs; Simultaneous ℋ2/ℋ∞ synthesis (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-009-9527-2

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