Model reduction via frequency weighting approach

Frequency weighted Gramians and a state weighted model reduction algorithm are proposed. The frequency weighted Gramians are defined in the frequency domain which have frequency weighting factors to accentuate the input-output behavior of the interested states in some frequency range. The algorithm is basically based on a state weighting technique due to frequency weighted Gramians differently from other algorithms that weights inputs or outputs. The concerned state has more influence on the reduced system in the range of the frequency weighted, resulting in small model reduction errors with little sacrifice in performance.