State Feedback Controller Design of Stochastic Singular Systems with Discontinuities

In this paper, the problem of controller design for Markovian singular systems with discontinuities (MSSD) is investigated. Sufficient conditions to guarantee that the unforced system is regular, impulse-free and stochastically stable in mean square sense with an norm bound constraint, are provided. The derived conditions are expressed in terms of a set of linear matrix inequalities (LMIs), which can be solved by using existing linear algorithms. Also, based on this result, a memoryless State feedback control which ensures the piecewise regularity, the absence of impulsive behavior and the stochastic stability in mean square sense of the closed-loop systems, is proposed by combining the LMI technique, the cone complementarity approach and the sequential linear programming matrix method (SLPMM). A numerical example is given to demonstrate the effectiveness of the proposed methods.