Stabilization of Discrete-Time Hidden Semi-Markov Jump Linear Systems With Partly Unknown Emission Probability Matrix

Abstract

This paper studies the stabilization problem for a class of discrete-time hidden semi-Markov jump linear systems with partly unknown emission probability matrix. By virtue of the improved semi-Markov kernel approach and emission probability approach, the less conservative sufficient stability conditions are proposed on the basis of emission probability matrix with partly unknown elements. With the aid of an improved eliminating matrix product technique, the nonlinear matrix terms with respect to system coefficient matrix and controller gain matrix in the above conditions are decoupled into the linear matrix forms, and the numerically testable existence conditions of the observed mode dependent controller for the corresponding closed-loop systems are obtained. An example is given to illustrate the effectiveness of our results.