On stability of constrained receding horizon control with finite terminal weighting matrix

In this paper, a new stabilizing receding horizon control, based on a finite input and state horizon cost with a finite terminal weighting matrix, is proposed for time-varying discrete linear systems with constraints. We propose matrix inequality conditions on the terminal weighting matrix under which closed loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints. We show that such a terminal weighting matrix can be obtained by solving an LMI (Linear Matrix Inequality). In the case of constrained time-invariant systems, an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints. Using the invariant ellipsoid constraints, a feasibility condition of the optimization problem, is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control.