线性离散时变系统的离散Walsh函数模型降阶  

Order Reduction of Discrete Walsh Functions Models for Linear Discrete Time-Varying Systems

作　　者：唐升国 蒋耀林[2,1] 王兆鸿 TANG Sheng-guo;JIANG Yao-lin;WANG Zhao-hong(College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830046,China;School of Mathematics and Statistics,Xian Jiaotong University,Xian Shaanxi 710049,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《计算机仿真》2023年第7期373-377,共5页Computer Simulation

基　　金：国家自然科学基金(11871393);陕西省重点研发计划国际合作项目(2019KWZ-08)。

摘　　要：为解决线性离散时变系统的模型降阶问题,提出两种基于离散Walsh函数的模型降阶方法:方法1,采用递推法得到线性离散时变系统状态方程的解,并由此得到状态变量的离散Walsh函数系数矩阵,借助所得系数矩阵构造正交投影矩阵,进而得到降阶系统。方法2,将系统在离散Walsh函数所构成的空间中展开,通过求解矩阵方程得到离散Walsh函数系数矩阵,由此系数矩阵和非零初值得到正交投影矩阵并构造降阶系统。理论分析表明两种方法所得降阶系统分别能够匹配原始系统一定数目的展开系数。数值算例验证了所提方法的可行性和有效性。In this paper,we propose two model order reduction(MOR)methods based on discrete Walsh functions for linear discrete time-varying systems.Method 1:Using the recursive method to obtain the solutions of the state equation of a linear discrete time-varying systems;The reduced order system is obtained by the orthogonal projection matrix that is constructed by using the discrete Walsh functions coefficient matrix.Method 2:The original system is extended in the space spanned by discrete Walsh functions,and the discrete Walsh functions coefficient matrix is computed from a matrix equation.Similarly,the reduced order system is constructed by the orthogonal projection matrix that is obtained by the coefficient matrix and nonzero initial values.The theoretical analysis shows that the reduced order systems constructed by the two MOR methods can match a certain number of expansion coefficients of the original system,respectively.A numerical example was given to illustrate the feasibility and effectiveness of the proposed methods.

关 键 词：线性离散时变系统 模型降阶 离散函数 系数匹配 

分 类 号：O29[理学—应用数学]