On subspace balanced realization and model order reduction for nonlinear interconnected systems

This paper is concerned with a nonlinear extension of the author´s former result on balanced realization and model order reduction for feedback interconnected systems. This paper proposes novel notions of subspace balanced realization, subspace singular values and subspace singular vectors. They characterize the balanced realization of a subsystem with respect to an input-output map of the whole feedback system. Balanced truncation based on the proposed subspace balanced realization gives us a reduced order subsystem in such a way that the reduced feedback system maintains its stability. It can be readily applicable to a controller reduction problem.