Applications of the singular perturbation approximation of balanced systems

This paper considers the use of balanced realizations in the context of plant and controller order reduction. The emphasis is placed on reduced order models obtained from the singular perturbation approximation of the balanced realization of a system. The reduced system thus obtained (sometimes simply referred to as a balanced residualization), unlike a truncated system or an optimal Hankel-norm approximation, maintains the steady-state gain of the system. In addition, the singular perturbation approximation of a balanced system is seen to give good matching at low and medium frequencies. This is favourable with regards to both plant and controller reduction. The method is demonstrated on examples and detailed comparisons made with balanced truncation and optimal Hankel-norm approximation