This paper investigates time domain model order reduction of discrete-time bilinear systems with inhomogeneous initial conditions. The state of the system is approximated by the power series associated with the Charlier polynomials and the recurrence relation of the expansion coefficients is derived. The expansion coefficients are orthogonalized to construct the projection matrix by the modified multi-order Arnoldi method. The output of the resulting reduced order system maintains a certain number of expansion coefficients of the original output, and the error estimation of the reduced order system is briefly discussed. Due to the fact that the projection matrix involves the information of initial conditions, the proposed method can well reduce discrete-time bilinear systems with inhomogeneous initial conditions. Two numerical examples are employed to illustrate the effectiveness of the proposed method.

本文研究了具有非齐次初始条件的离散时间双线性系统的时域模型降阶问题。系统状态由与 Charlier 多项式相关的幂级数近似，并推导出展开系数的递推关系。通过改进的多阶 Arnoldi 方法对展开系数进行正交化以构建投影矩阵。得到的降阶系统的输出保持了原输出一定数量的展开系数，简要讨论了降阶系统的误差估计。由于投影矩阵包含初始条件信息，该方法可以很好地减少初始条件非齐次的离散时间双线性系统。