Balancing free reduction algorithm for singularly perturbed stable/unstable systems

摘要

A generalized balancing free reduction algorithm which combines the advantages of balancing free, square root and singular perturbation approximation techniques is proposed in this paper. The proposed technique is based on the singular value decomposition of Cholesky factors of controllability and observability gramians. The merit of the proposed algorithm is, it is almost free from all the deficiencies of Moore's balanced realization and truncation and removes the necessity of using bilinear-transformation and hence the occurrence of two-fold error is avoided. The applicability of the proposed technique has been illustrated with the help of some benchmark examples and reduced models obtained produce far better results than the existing ones.