Advanced global optimization algorithms for parameterized LMIs

Parameterized linear matrix inequalities (PLMIs) frequently arise in analysis and synthesis problems of robust control theory. However, in contrast to linear matrix inequalities (LMIs) which are convex optimization problems with available efficient polynomial-time interior-point methods, PLMIs are highly nonconvex and thus are very hard to solve. In this paper, we exploit partial convexity properties of PLMIs that are useful for optimization purposes. We then propose various global optimization algorithms, practical and efficient, as resolution methods. The tools so constructed are finally validated on some open problems in robust control.