Constrained quadratic control for Markov jump systems with multiplicative noise

In this paper, the constrained quadratic control problem of discrete-time Markov jump systems with multiplicative noise in both state and control input is studied. An asynchronous hidden Markov model with a partially known transition probability is constructed as the controller model of the system taking into account the mode mismatch between the system and the controller and the unavailable transition probability of the controller. Under the feedback control of the asynchronous controller, the conditions for the system to achieve stochastic stability are given by using the linear matrix inequality method. In addition, when the initial conditions satisfy the invariant set of constraints, the state and control sequences are guaranteed to satisfy the desirable constraints. Solving the linear matrix inequality optimization problem also yields a cost upper bound for quadratic functions. The effectiveness and superiority of the theoretical results are finally validated by numerical instances.