Stochastic stabilization of singular systems with Markovian switchings

This paper studies the stochastic stabilization problem for a class of singular Markovian jump system. The aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular Markovian jump system (SMJS). A new kind of stochastic controller only in the diffusion part is proposed such that the closed-loop system has a unique solution and is almost surely exponentially admissible. New sufficient condition for the existence of such a controller is given as linear matrix inequalities (LMIs). Based on this, more extensions to transition probability matrix (TPM) with elements partially unknown and system states partially observable are developed. A numerical example is used to demonstrate the effectiveness of the proposed methods.