Poles residues descent algorithm for optimal frequency-limited ℋ2 model approximation

Model approximation of multiple-inputs/multiple-outputs (MIMO) linear dynamical systems over a bounded frequency range can be expressed as an optimization problem in terms of the frequency-limited ℋ
₂
-norm. In this paper, a new formulation of the frequency-limited ℋ
₂
model approximation error is presented and its gradient derived. It is then used in a descent algorithm which does not require to solve any Lyapunov equations but one eigenvalue problem for the full-order model. The efficiency of the method is illustrated through numerical benchmarks.