Stabilization for Markovian Jump Distributed Parameter Systems With Time Delay

Abstract

The problems of stochastic stability and stabilization for a class of Markovian jump distributed parameter systems with time delay are researched in this paper. First, taking advantage of a combination of Poincare inequality and Green formula, a stochastic stability criterion is presented by a linear matrix inequality (LMI) approach. Then, a state feedback controller is designed. Based on the proposed results, the sufficient conditions of the close-loop systems' stochastic stability are given in terms of a set of LMIs by constructing the appropriate Lyapunov functionals, calculating the weak infinitesimal generator, and using the Schur complement lemma. The sufficient conditions could be solved directly and applied to engineering practice conveniently. The obtained results generalize and enrich the theory of distributed parameter systems with time delay. The model of Markovian jump distributed parameter systems is more fitting the actual systems' requirements and has wider application scope. Finally, numerical examples are used to demonstrate the validity of the method.