状态空间时滞系统稳定性检验的二维方法

2-D Approach for Stability Test of State-Space Time-Delay Systems

由于时滞系统的特征根有无限多个,所以检验时滞系统的稳定性是困难的.为解决这一问题,本文提出用二维方法检验时滞系统的稳定性.对给定时滞系统的特征多项式,根据时滞构造适当阶次的二维s＿z混合多项式,则该二维s＿z混合多项式的稳定性可确保该时滞系统为稳定的.本文提出二维Routh＿Schur检验用于二维s＿z混合多项式的稳定性的代数检验.应用举例说明了本文所提方法的可行性.

Since the number of eigenvalues of the systems are infinite, it is difficult to determine the stability of state_space time_delay systems. To solve the problem of stability test of the systems, we develop a 2_D approach for the stability test of state_space time_delay systems. Constructing a 2_D s_z hybrid polynomial with suitable order based on the time_delay for the characteristic polynomial of the given time_delay system, we show that the stability of the 2_D polynomial can ensure the delay system to be stable, and we develop a 2_D Routh_Schur test for the stability of 2_D s_z hybrid polynomial. Examples have been given to demonstrate the applicability of our new approach.