An approach to H_{2, ω} model reduction on finite interval for bilinear systems

In this paper, we discuss the problem of the optimal H₂ model order reduction (MOR) on a given frequency interval for bilinear systems. We first define the H_{2, ω} norm for bilinear systems. And it is shown that the H_{2, ω} norm for the bilinear system can be computed by its frequency-limited controllability Gramian or the frequency-limited observability Gramian. One of our contributions is that the necessary conditions for the order-reduced bilinear system to be H_{2, ω} optimal are derived. Thereby, an iterative algorithm is proposed to construct the order-reduced bilinear system with high accuracy in the selected frequency interval. Numerical examples demonstrate the effectiveness of our algorithm.