利用奇异值分解的二阶递归系统数值稳定性方法

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.

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

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.