Difference of multiconvex relaxation of parameterized LMIs: control applications

Relaxation of an optimization problem under parametrized LMIs (PLMIs) constraint is discussed in this paper. The relaxation methods are based on convexfication using difference of convex (d.c.) and multiconvexfication techniques, thus the relaxed problems become numerically tractable. The d.c. relaxation method is generalized and is imported into the multiconvex relaxation method, then the difference of multiconvex relaxation is naturally defined. These two relaxation methods are applied to stability and L/sub 2/ gain analysis of linear parameter varying (LPV) systems based on affine parameter-dependent Lyapunov function and are discussed from an amount of computation viewpoint. Numerical examples are illustrated for the application to show the effectiveness of these methods.