Robust stability, stabilization and H-infinity control of time-delay systems with Markovian jump parameters

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Mahmoud, Magdi S and Shi, Peng (2003) Robust stability, stabilization and H-infinity control of time-delay systems with Markovian jump parameters. International Journal of Robust and Nonlinear Control, 13 (8). pp. 755-784. ISSN 1049-8923


In this paper, the problems of stochastic stability and stabilization for a class of uncertain time-delay systems with Markovian jump parameters are investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process. The parametric uncertainties are assumed to be real, timevarying and norm-bounded that appear in the state, input and delayed-state matrices. The time-delay factor is constant and unknown with a known bound. Complete results for both delay-independent and delay-dependent stochastic stability criteria for the nominal and uncertain time-delay jumping systems are developed. The control objective is to design a state feedback controller such that stochastic stability and a prescribed H1-performance are guaranteed. We establish that the control problem for the time-delay Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled algebraic Riccati inequalities or linear matrix inequalities. Extension of the developed results to the case of uncertain jumping rates is also provided.

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Item type Article
DOI 10.1002/rnc.744
Official URL
Subjects Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Keywords ResPubID18916, time-delay systems, Markovian jump parameters, H-infinity state feedback, stochastic stability, uncertain parameters
Citations in Scopus 124 - View on Scopus
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