Stability analysis of multivariable feedback systems with control input saturation

We propose a new algorithm for approximating the largest invariant stability domain of a multivariable feedback system with control input saturation. Our approach is based on a polytopic covering of the considered saturated plant and the use of Lyapunov functions of the Lur´e and Postnikov type. The use of such functions is expected to relax part of the conservatism introduced by quadratic approaches. The proposed method offers appealing numerical properties since it lies on the resolution of linear matrix inequalities. Finally , the applicability of our algorithm is demonstrated by an example