Balanced Realizations for Linear Systems: A Variational Approach

Abstract

This paper develops a new geometric approach to balanced realizations, which enables balanced realizations for arbitrary linear systems to be defined and studied. For an arbitrary (unitarily invariant) strictly plurisubharmonic function on the set of realizations of a given transfer function, the class of realizations is considered that minimizes the function. Based on results from invariant theory and complex analysis, a general theorem on the existence and uniqueness properties of such function-minimizing realizations is derived. If the function is the sum of the traces of the controllability and observability gramians, the usual class of balanced realizations is obtained. Other choices of functions yield different, new classes of function-minimizing realizations.