Balanced realization and model reduction of singular systems

Abstract

The problem of balanced realization and model reduction of a singular system of the form E[xdot] = Ax + Bu, where E is a singular matrix, is considered. Using coordinate transformation, which can be computed by performing singular value decomposition of E, we derive our first approach to the balancing of singular systems. The second approach is based on standard form decomposition of singular systems to slow and fast subsystems and performing balanced realization on the decomposed model. In this sense model reduction can be established in two steps: first, by decomposing the singular system and second, by performing balancing transformation on the decomposed subsystems.