| Abstract: | A wide variety of problems in control system theory fall within the class of parameterized Linear Matrix Inequalities (LMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. However, in contrast to LMIs, parameterized LMI (PLMIs) feasibility problems involve infinitely many LMIs hence are very hard to solve. In this paper, we propose several effective relaxation techniques to replace PLMIs by a finite set of LMIs. 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 and illustrated by examples. Copyright © 1999 John Wiley & Sons, Ltd. |
