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Reducing order of large-scale systems by extended balanced singular perturbation approximation

In this paper, a simplified approach for model order reduction, based on balanced singular perturbation approximation (BSPA) technique, is explored which is applicable for linear time invariant, minimal/non-minimal continuous/discrete-time systems. An extension of BSPA technique is proposed for order reduction of unstable systems. For reduction of unstable system, a system decomposition algorithm using real Schur transformation is given to decompose the unstable system into stable and unstable parts. Reduced order model of original unstable system is obtained by reducing the decomposed stable part by BSPA technique and directly adding it to decomposed unstable part. The algorithm is illustrated with MATLAB-based computer-simulated results in both time and frequency domains.