Stabilization of singular Markovian jump systems via switching probability rate design

This paper is concerned with the stabilization problem of singular Markovian jump systems, where both of the switching probability rate and state feedback gain are designed. A new sufficient condition is proposed to guarantee the stochastic admissibility of the unforced singular Markovian jump systems, which also characterizes the switching probability rete. Then, a condition for the existence of the desired controller gain and probability rate matrix is established as in terms of linear matrix inequalities with some equation constraints. Based on this, extensions to polytopic uncertainty and element-wise uncertainty cases are also obtained. A numerical example is used to demonstrate the effectiveness of the proposed methods.