Constrained MPC of uncertain discrete-time Markovian jump linear systems

This paper is concerned with constrained model predictive control (MPC) of discrete-time Markovian jump linear systems (MJLSs) subject to polytopic uncertainties in system matrices, where the constraints consist of hard mode-dependent constraints on inputs and states. The multi-step mode-dependent state-feedback control law is utilized to minimize an upper bound on the expected worst-case infinite horizon cost function. To reduce conservatism meanwhile guaranteeing the recursive feasibility, the minimization of the expected worst-case infinite horizon cost function and the constraints handling are dealt with in a separate way. The resulting algorithm is proved to guarantee both the mean square stability and the satisfaction of the hard mode-dependent constraints on inputs and states. Finally, a numerical example is given to illustrate the proposed results.