Stability & feasibility of constrained receding horizon control

In this paper we present an approach to test stability and feasibility of discrete-time LTI systems subject to constrained optimal control. The analysis is based on the feedback solution of the constrained optimal control problem formulated in a Receding Horizon fashion. The validation procedure consists of two independent parts. For stability, a piecewise quadratic Lyapunov function is computed by solving LMIs. Sufficient conditions for the existence of such functions are given. To guarantee feasibility, an efficient algorithm for computing invariant subsets of piecewise affine systems is presented. Finally, we demonstrate how this method may serve to obtain controllers of low complexity.