The stability analysis and control design problems for a class of discrete-time hidden semi-Markov jump singular systems

This paper studies the stability analysis and controller design problems for a class of discrete-time hidden semi-Markov jump singular systems. Firstly, by comprehensively utilizing the singular matrix decomposition method, the semi-Markov kernel approach, emission probability approach, matrix power elimination technique, and coefficient matrix restoring technique, a novel sufficient conditions with a set of linear inequalities of the original system coefficient matrices that guarantees regularity, causality, and σ-mean square stability can be constructed. Secondly, by combining the matrix congruent transformation method and the matrix decoupling method, the existence condition of the state feedback asynchronous controllers for such systems can be obtained. Finally, a numerical example is given to verify the effectiveness of our results.