Quadratic Stabilization of Discrete -

In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space known as clusters the plant is assumed to be an element in a polytope which vertices (local models) are aane systems. In the clusters containing the origin in their closure, the local models are restricted to being linear systems. The clusters cover the region of interest in the state-space. An aane state-feedback is associated with each cluster. By utilizing the aan-ity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs) combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise aane state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.