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Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers. (English) Zbl 1137.93421
Summary: This paper is concerned with the stabilization problem for a class of discrete-time Markovian jump linear systems with time-delays both in the system state and in the mode signal. The delay in the system state may be time-varying. The delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system. We first show that the resulting closed-loop system is a time-varying delayed Markovian jump linear system with extended state space. Then a sufficient condition is proposed for the design of a controller such that the closed-loop system is stochastically stable. Finally, numerical simulation is used to illustrate the developed theory.

MSC:
93E15 Stochastic stability in control theory
93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
60J05 Discrete-time Markov processes on general state spaces
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