Robust model predictive control for uncertain state delayed system using polytope dependent Lyapunov function

In this paper, we propose a method of computing a improved model predictive control (MPC) law for uncertain state delayed system with unknown bounded delay term and input constraints. The proposed method improves feasibility characteristics and system tracking performance by deriving a sufficient condition for the cost monotonicity using polytope dependent Lyapunov function corresponding to a different vertex. The control problem is formulated as a minimization of the upper bound of infinite horizon cost function satisfying the sufficient conditions. The polytope dependent Lyapunov function yield less conservative sufficient condition in terms of linear matrix inequalities (LMIs) so that it allows to design a more robust MPC. A numerical example is included to illustrate the effectiveness of the proposed method.