Observer-Based Controller Design for Singular Stochastic Markov Jump Systems with State Dependent Noise

This paper is concerned with the problem of observer-based controller design for singular stochastic Markov jump systems with state-dependent noise. Two concepts called "non-impulsiveness" and "mean square admissibility" are introduced, which are different from previous ones. Sufficient conditions for the open-and closed-loop singular stochastic Markov jump systems with state-dependent noise to be mean square admissible are provided in terms of strict LMIs. The controller gain and the observer gain which guarantee the resulting closed-loop error system to be mean square admissible are obtained in turn by solving the strict LMIs. A numerical example is presented to show the efficiency of the design approach.