H₂ model order reduction based on gramians of discrete-time bilinear systems

In this paper, on the basis of gramians, H₂-optimal model order reduction of discrete-time bilinear dynamic systems is investigated. First, based on the reachability gramian and the observability gramian, the H₂-optimal necessary conditions of the discrete-time bilinear system are derived and the corresponding algorithm is proposed. When the algorithm is convergent, the resulting reduced system satisfies the necessary conditions. Then, for the single-input and single-output system, the H₂-optimal necessary conditions based on the generalized cross gramian are presented and the related algorithm is accordingly generated. Similarly, the convergent algorithm can make the reduced system satisfy the necessary conditions. Finally, two numerical examples are employed to illustrate the effectiveness of the proposed methods.