基于符号数学工具箱的Routh稳定判据及应用

离散系统稳定性判据是计算机控制系统分析与设计的重要内容。为了使连续系统的Routh判据能用于离散系统，需借助双线性变换把Z平面转换成w平面。文章提出借助MATLAB符号数学工具箱对双线性变换和Routh表系数求解过程实现CAD；对Routh表中第一列元素为零的两种特殊情况作了深入讨论；还探讨了Routh判据的应用，通过计算系统参变量，确定系统稳定时参变量的取值范围。和理论分析结果比较，证明本文介绍的CAD方法是正确的。

The Routh Stability Criterion and Its Application Based on Symbolic Math Toolbox

The stability criterion of discrete systems is an important part in the analysis and design of the computer control system. While Routh stability criterion for continuous systems used in discrete system, the z plane has to be converted into the w plane by bilinear transform. A CAD method is presented in this paper, the calculating process are achieved automatically using symbolic math toolbox on MATLAB. Two special cases that the elements are zero on the first column of Routh table are discussed detailedly and found out a solution. This paper discusses the application of Routh criterion, the numerical range of system variable is confirmed by parameter account and ensured the system into stable state. The result compare shows that this method is correct.