Optimality properties of balanced realizations: Minimum sensitivity

Abstract

It has been well established that the so-called balanced state space realizations of linear time-invariant systems have certain desirable computational properties. But the complete relationship between balanced realizations and the general parameter sensitivity problem is not yet fully appreciated. In this paper we present a geometric approach to the robust design problem and its solution using a specific optimality criterion. In particular, for discrete-time linear systems, a minimum sensitivity parameterization of a linear system with a given input-output relationship will be linked to the balanced realization.