Problems of computing norms of 2D systems

Abstract

The computation of the H_∞ and H₂ norms of 2D systems (systems whose dynamic state depends on two independent variables) can be reduced to algebraic problems underlain by parametrized linear matrix inequalities, which have to hold for all parameter values. Available methods for solving such problems based on their interpretation in terms of nonnegative polynomials are poorly scaled since the sizes of auxiliary problems grow rapidly. In this paper, solution methods are presented that are simpler and more efficient as compared with well-known results.