Stability analysis and control synthesis with D.C. relaxation of parameterized LMIS

Relaxation of an optimization problem under parametrized LMI constraint is discussed in this paper. Relaxation methods are based on convexfication using difference of convex and multiconvex techniques, thus the relaxed problems become numerically tractable. The d.c. relaxation is generalized and is imported into the multiconvex relaxation, then the difference of multiconvex relaxation is naturally defined. These two relaxation methods are applied to stability and state-feedback control synthesis of linear parameter varying systems. Numerical examples are illustrated for the applications to show the effectiveness of these methods.