H₂ model order reduction for bilinear systems based on the cross gramian

The H₂ optimal model order reduction on the basis of the cross gramian for a given single-input and single-output (SISO) bilinear system is discussed in this article. According to the cross gramian, the expression of H₂ norm for the SISO bilinear system can be represented. Then, taking advantage of the partial derivative, we can derive the necessary conditions of the H₂ optimality for the reduced order bilinear system. From the necessary conditions, the coefficient matrices of the H₂ optimal reduced order system can be constructed. After that, we propose an iterative algorithm based on the cross gramian. When the algorithm is convergent, the reduced order system can satisfy the necessary conditions. Finally, the numerical examples exhibit the effectiveness of our algorithm.