Constrained robust model predictive control for time-delay descriptor systems with linear fractional uncertainty

Abstract

This paper addresses the robust model predictive control (MPC) for a class of time delay descriptor systems with linear fractional uncertainty and input constrains. The systems are transferred to the piecewise continuous descriptor systems and a piecewise constant control sequence is calculated by minimizing the worst-case quadratic objective function. At each sampling internal, by means of Lyapunov theory and optimization theory, the optimal problem with infinite horizon objective function is reduced to a convex optimization problem involving linear matrix inequalities. The sufficient conditions for the existence of the state feedback control are derived and expressed as linear matrix inequalities. Further, an iterative model predictive control algorithm is proposed for the on-line synthesis of state feedback controllers with the conditions guaranteeing that the closed-loop descriptor systems are regular, impulse-free and robust stable. Finally, a numerical example is presented to show the efficiency of the proposed approach