Robust receding horizon control of discrete-time Markovian jump uncertain systems

This paper proposes a receding horizon control scheme for a set of uncertai n discrete-time linear systems with randomly jumping parameters described b y a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets. The control scheme for the underlyin g systems is based on the minimization of an upper bound on the worst-case infinite horizon cost function at each time instant. It is shown that the m ean square stability of the proposed control system is guaranteed under som e matrix inequality conditions on the terminal weighting matrices. The prop osed controller is obtained using semidefinite programming.