Time-weighted balanced stochastic model reduction

A new relative error model reduction technique for linear time invariant (LTI) systems is proposed in this paper. Both continuous and discrete time systems can be reduced within this framework. The proposed model reduction method is mainly based upon time-weighted balanced truncation and a recently developed inner-outer factorization technique. Compared to the other analogous counterparts, the proposed method shows to provide more accurate results in terms of time weighted norms, when applied to different practical examples. The results are further illustrated by a numerical example.