Frequency-weighted ℌ2-pseudo-optimal model order reduction

Abstract

Abstract The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we investigate the frequency-weighted $\mathcal{H}_2$-pseudo-optimal model order reduction problem wherein a subset of the optimality conditions for the local optimum is attempted to be satisfied. We propose two iteration-free algorithms, for the single-sided frequency-weighted case of $\mathcal{H}_2$-model reduction, where a subset of the optimality conditions is ensured by the reduced system. In addition, the reduced systems retain the stability property of the original system. We also present an iterative algorithm for the double-sided frequency-weighted case, which constructs a reduced-order model that tends to satisfy a subset of the first-order optimality conditions for the local optimum. The proposed algorithm is computationally efficient as compared to the existing algorithms. We validate the theory developed in this paper on three numerical examples.