Asynchronous Control for Discrete-Time Markovian Jump Systems With Multiplicative Noise

In this note, the guaranteed cost control problem for discrete-time Markovian jump systems with state and input multiplicative noise is solved. Since the model mismatch problem often exists in system modes and controller modes, an asynchronous controller is presented to make the system stochastically stable. By using of the linear matrix inequality techniques, an optimization solution can be obtained, such that the quadratic cost function can be minimized, meanwhile the expectation of the state and control can be guaranteed in a constraint set.