Receding Horizon Control for Uncertain Markov Jump Linear Systems with Time Delay and Actuator Saturation

A robust receding horizon control (RHC) scheme is developed for uncertain discrete-time Markov Jump Linear Systems (MJLS) with time delay and actuator saturation where the system uncertainties and jumping transition probabilities are assumed to belong to some convex sets. Firstly, when time delay is considered, a sufficient condition of minimizing upper bound of the cost function and mean square stability of the closed-loop system are established based on the Lyapunov Krasovskii function which depend on the current time jump mode. At each sampling time, an optimal control gain can be obtained by solving the semi-definite programming (SDP) problem. Then, the proposed strategy is extended to design robust RHC scheme for uncertain MJLS with both time delay and actuator saturation. Moreover, the domain of attraction can be estimated through a modified invariant ellipsoid. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.