Balanced approximation of two-dimensional and delay-differential systems

Abstract

A generalized balanced approximation method for reducing two-dimensional (2-D) and delay-differential models is given. This is possible because of the form the gramians of such systems take. In particular it is shown that the reachability and observability gramians can be expressed as integrals of a certain system-related function along the imaginary axis or unit circle of the complex plane. The gramians provide two sets of system invariants which lead in a natural way to the concept of a generalized balanced realization, which in turn leads to a way to accomplish model reduction.