Accuracy Enhancing Methods for the Frequency-Weighted Balancing Related Model Reduction

Abstract

In this paper we propose an effcient computational approach to minimize the H-infinity-norm of a transfer-function matrix depending affinely on a set of free parameters. The minimization problem, formulated as a semiinfinite convex programming problem, is solved via a relaxation approach over a finite set of frequency values. In this way, a significant speed up is achieved by avoiding the solution of high order LMIs resulting by equivalently formulating the minimization problem as a high dimensional semidefinite programming problem. Numerical results illustrate the superiority of proposed approach over LMIs based techniques in solving zero order H1-norm approximation problems.