Relaxations of parameterized LMIs with control applications

A wide variety of problems in control system theory fall within the class of parameterized linear matrix inequalities (LMI), that is, LMI whose coefficients are functions of a parameter confined to a compact set. However, in contrast to LMI, parameterized LMI (PLMI) feasibility problems involve infinitely many LMI hence are very hard to solve. In this paper, we propose several effective relaxation techniques to replace PLMI by a finite set of LMI. The resulting relaxed feasibility problems thus become convex and hence can be solved by very efficient interior point methods. Applications of these techniques to different problems such as robustness analysis, or linear parameter-varying (LPV) control are then thoroughly discussed