平面系统稳定性的间接方法*

Indirect Method for Stability of Plane Systems

中文关键词  Routh 判据  区间矩阵  Jacobian猜想  稳定吸引域  滑模控制

英文关键词  Routh criteria  interval matrixes  Jacobian conjecture  stability attraction reging  sliding mode control

中文摘要

      利用Routh 判据得到的间接检验矩阵特征值的方法讨论平面系统的稳定性问题，对于线性系统，该方法给出平面区间矩阵稳定性的充要条件.对于非线性系统，Jacobian 猜想的已知结果[5]，该方法给出平面非线性系统稳定吸引域估计的一种算法.最后，该估计被利用于高维系统二维滑动模的设计.

英文摘要

      Using Routh criteria the paper investigates the problems of stability of plane systems via indirect verification of the eigenvahues of matrixes. For linear systems, the method provides necessary and suffcient conditions for the stability of plane interval matrixes. In nonliear case, based on the results of [5]about the Jacobian conjecture, the method gives two algonrithms for estimating the stability attracton region of plane systems. Finally, such estimations are used to design two dimensional sliding mode of higher degree control systems.