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A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates. (English) Zbl 1326.93111
Summary: This paper is devoted to investigating the problem of robust sliding mode control for a class of uncertain Markovian jump linear time-delay systems with generally uncertain transition rates (GUTRs). In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. A sliding mode control law is developed to drive the state trajectory of the closed-loop system to the specified linear switching surface in a finite-time interval in spite of the existing uncertainties, time delays and unknown transition rates. Finally, an example is presented to verify the validity of the proposed method.

MSC:
 93D21 Adaptive or robust stabilization 93E15 Stochastic stability in control theory 93B12 Variable structure systems 60J75 Jump processes (MSC2010)
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