Relaxations of Parameterized LMIs with Control Applications
نویسندگان
چکیده
A wide variety of problems in control system theory fall within the class of parameterized Linear Matrix Inequalities (LMIs), that is, LMIs whose coecients are functions of a parameter conned to a compact set. However, in contrast to LMIs, param-eterized LMI (PLMIs) feasibility problems involve innitely many LMIs hence are very hard to solve. In this paper, we propose several eective relaxation techniques to replace PLMIs by a nite set of LMIs. The resulting relaxed feasibility problems thus become convex and hence can be solved by very ecient interior point methods. Applications of these techniques to dierent problems such as robustness analysis, or Linear Parameter-Varying (LPV) control are then thoroughly discussed and illustrated by examples.
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