Relative error model reduction via time-weighted balanced stochastic singular perturbation

A new mixed method for relative error model reduction of linear time-invariant systems is proposed in this paper. This order reduction technique is mainly based upon the time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared to the other analogous counterparts, the proposed method provides more accurate results in terms of time-weighted norms when applied to the practical examples. It is shown that important properties of the time-weighted stochastic balanced reduction technique are extended to the mixed reduction method by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of compact disc player and a model of the atmospheric storm track.