Robust model predictive control for discrete uncertain time-varying systems with delay

In this paper, we present a method for synthesizing a robust model predictive control for uncertain time-varying systems with state delay. The goal is to design, at each sampling time, a state feedback control law that minimizes an upper bound of the worst-case objective function, subject to constraints of control inputs. The worst-case performance is defined as an infinite-horizon quadratic function of states and control inputs. In order to guarantee robust performance, the method uses multiple Lyapunov-Krasovskii functions each of which corresponds to a different vertex of the uncertainty polytope. The state feedback design problem is cast as convex optimization involving linear matrix inequalities which can be efficiently solved. The proposed technique yields an improved performance and less conservative than the robust model predictive control technique using a single Lyapunov-Krasovskii function. A numerical example is provided to illustrate the effectiveness of the control algorithm.