Stochastic stability for discrete-time antilinear systems with Markovian jumping parameters

In this study, the discrete-time antilinear systems with Markovian jumping parameters are investigated. The concept of stochastic stability is extended to the context of discrete-time Markovian jump (DTMJ) antilinear systems. By using stochastic Lyapunov approach, the authors derive some necessary and sufficient conditions for a DTMJ antilinear system to be stochastically stable in terms of coupled anti-Lyapunov matrix equations. In addition, two types of iterative algorithms are proposed to solve these coupled anti-Lyapunov matrix equations. Finally, some numerical examples are given to show the efficiency of the proposed algorithms and potential applications of the obtained results on antilinear systems.