Robust stability on discrete-time nonhomogeneous singular semi-Markov jump systems with a polytopic method

Abstract

This paper investigates the issues of robust stability analysis on discrete-time nonhomogeneous singular semi-Markov jump systems (SMJSs) with a polytopic method. The robust stability problem is considered based on two decomposition forms, which are respectively the standard form based on differential matrix and the Weierstrass standard form. First, without considering disturbance, in terms of joint spectral radius, necessary and sufficient (NS) conditions for mean square stability (MSS) are presented for discrete-time nonhomogeneous singular SMJSs when its transition probability matrix (TPM) is fixed by a polytopic set of stochastic matrices, and the equivalence of MSS, exponential MSS and stochastic stability is also proved. Then, when the system is disturbed by bounded disturbance, necessary and sufficient conditions for robust stability are also obtained. Lastly, examples are given to illustrate the effectiveness of the proposed results.