Parametrized Matrix Inequalities in Analysis of Linear Dynamic Systems

Abstract

Problems that can be reduced to polynomial and parametrized linear matrix inequalities are considered. Such problems arise, for example, in control theory. Well-known methods for their solution based on a search for nonnegative polynomials scale poorly and require significant computational resources. An approach based on systematic transformations of the problem under study to a form that can be addressed with simpler methods is presented.