Monotonic relaxation for robust control: new characterization

Linear matrix inequalities depending on parameters (PLMI) over a box arise frequently with the analysis and synthesis problems in robust control. However, PLMIs are equivalent to systems of infinitely many linear matrix inequalities (LMIs) and the already well known convexity based approach reduces to solve them by a finite exponential order number of LMIs. In this paper we propose a novel approach based on monotonic optimization which allows one to solve them by a finite polynomial order number of LMIs. The viability of our approach is illustrated by numerical examples with robust stability with real uncertainties and H_∞ control for linear parameter varying systems