LMI-based control design for discrete polytopic LPV systems

This paper presents two LMI-based designs for the stabilization and regulator problems of polytopic discrete linear parameter-varying (LPV) systems. The main advantage of the new approaches is that they are based on parameter-varying Lyapunov functions. Different Lyapunov functions are computed for each vertex of the polytope and the global Lyapunov function is a convex combination of local ones. The algorithms proposed are thus less conservative compared to the more usual approach of employing a common P matrix.