基于交叉Gram矩阵的离散周期系统模型降阶

Model Order Reduction Based on Cross Gramians of Discrete Periodic Systems

针对单输入单输出离散周期系统的模型降阶问题,提出了基于交叉Gram矩阵的奇异值分解截断模型降阶方法。首先,定义了离散周期系统的交叉Gram矩阵,并将离散线性时不变系统交叉Gram矩阵的相关性质推广到离散周期系统中。其次,基于交叉Gram矩阵,通过矩阵奇异值分解截断方法得到降阶系统。再次,利用输出多相采样传递函数证明了该方法与传统平衡截断方法的等价性。最后,数值算例验证了基于交叉Gram矩阵奇异值分解截断模型降阶方法是行之有效的。

On the basis of cross gramians,a singular value decomposition(SVD)truncation model order reduction method is proposed for the model order reduction of single input and single output(SISO)discrete periodic systems.Firstly,the cross gramians of the discrete periodic systems were defined,and the correlative properties of the cross gramians of the discrete linear time invariant systems were generalized to discrete periodic systems.Then,the cross gramians were employed to obtain the reduced order system and the matrix SVD truncation method was established.Moreover,the equivalence between the proposed method and the traditional balanced truncation method was demonstrated by the use of output sampling polyphase(OSP)transfer function.Finally,a numerical example illustrates the effectiveness of SVD truncation model order reduction method.