利用奇异值分解的二阶递归系统数值稳定性方法  

Numerical Stability Method of Second Order Recursive System Using Singular Value Decomposition

作　　者：付波[1] 刘济源 赵熙临[1] 徐光辉[1] 王子鹏 FU Bo;LIU Jiyuan;ZHAO Xilin;XU Guanghui;WANG Zipeng(School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, China)

机构地区：[1]湖北工业大学电气与电子工程学院,湖北武汉430068

出　　处：《华侨大学学报（自然科学版）》2017年第6期886-891,共6页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(61072130;51309094;61603127);国家教育部留学回国人员科研启动基金资助项目(20141685);湖北省科技厅重大科技专项项目(2013AE001)

摘　　要：为了简便地解决二阶递归系统的稳定性问题,将二阶递归系统转变为二阶离散时变线性系统,并讨论递归系统的稳定性.在二阶离散线性时变系统稳定性分析的基础上,利用奇异值分解(SVD),将其转化为参考信号(RS)系统.提出一个新的离散时变线性系统不稳定性的充分条件,并以离散正交Krawtchouk多项式与Jacobsthal数列递归式为主,讨论并推导出其在Ⅱ,Ⅳ象限上的变化情况和新的不稳定性判据.仿真结果验证了结论的准确性.In order to solve the problem of stability of second order recursive systemsimply,the second order recursive system is transformed into second order discrete time-varying linear system and the stability of recursive system is discussed.Based on the stability analysis of second-order discrete linear time-varying systems,converting it into a reference signal(RS)system by singular value decomposition(SVD).Based on discrete orthogonal Krawtchouk polynomials and the Jacobsthal series,a new sufficient condition for discrete time-varying linear instability is proposed.The changes and new instability codes in the second and fourth quadrants are discussed and deduced.The simulation results verify the conclusion accuracy.

关 键 词：Krawtchouk多项式 Jacobsthal数列 奇异值分解 递归系统 线性离散时变系统 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]