  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 H2-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 H2-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.
