Relaxation Methods of Parametrized LMIs Based on D.C. and Multiconvex Technique

Abstract

This paper gives relaxation methods reducing a feasibility or optimization problem under a parametrized linear matrix inequality constraint to a finite number of LMIs constraint. The methods are based on convexification of difference of convex (d.c.) and multiconvexification. We propose a generalized relaxation method of d.c. convexification and a unified relaxation method between d.c convexification and multiconvexification techniques. These methods are applied to stability analysis and L₂ gain analysis of parameter-dependent systems. Numerical examples are illustrated for each applications.