Reachable set synthesis for discrete-time Markovian jump systems with time-varying delay by partially asynchronous control

Abstract The problem of reachable set synthesis for discrete-time Markovian jump system-s(MJSs) with time-varying delay is researched. Different from the traditional controller, a kind of partially asynchronous controller is proposed. The normal system mode and the asynchronous mode are fully considered in the desired control law including delay state and delay-free state that happen asynchronously. Moreover, Bernoulli random variables are applied to represent the probability distribution of above two kinds of states. On these foundations, by employing Lyapunov theory and linear matrix inequalities(LMIs), a sufficient condition of the reachable set synthesis for MJSs under partially asynchronous control is given. Finally, a numerical example is provided to show the effectiveness of the proposed methods.