Model Order Reduction Methods for Discrete Systems via Discrete Pulse Orthogonal Functions

离散系统的离散脉冲正交函数模型降阶方法

This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.

针对离散线性和离散双线性系统,提出了基于离散脉冲正交函数的模型降阶方法.首先,将离散线性系统和离散双线性系统分别在离散脉冲正交函数所张成的空间中展开,得到两类关于系统状态变量展开系数的迭代关系式.然后,对所得两类迭代关系式分别实施修正的Arnoldi过程,得到正交投影矩阵,进而得到降阶系统.理论分析表明,所得降阶系统的输出变量能够匹配原始系统输出变量的有限个展开系数.最后,两个数值例子验证了所提模型降阶方法的可行性和有效性.