Robust model predictive control for uncertain singular systems with state delay

In this paper, we propose a model predictive control (MPC) law for a discrete time uncertain singular system with state delay and input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. Using zero equation with the free variable matrix, we derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. A numerical example is included to illustrate the effectiveness of the proposed method.