Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials

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.