On reachable set synthesis of delay Markovian jump systems under partially delay-dependent asynchronous control

This paper pays close attention to the reachable set synthesis problem for discrete-time delayed Markovian jump systems (DDMJSs) under partially asynchronous control. Different from the traditional controller, a class of partially asynchronous controller is proposed, where delay-free and delay states are comprised and cannot take place at the same time. In addition, Bernoulli variable is used to describe the probability distribution of the above two kinds of states, and the design of feedback controller is considered. On this basis, the sufficient conditions which the state feedback controller is existent are solved effectively by using linear matrix inequalities (LMIs). Furthermore, the results of reachable set synthesis are extended to the DDMJs with uncertain transition probabilities. Finally, several numerical simulations are given to show the effectiveness of the presented methods.