一种分数阶非线性系统稳定性判定定理的问题及分析

摘要

The research on the stability theory of fractional order nonlinear system has an important value for the application of synchronization and the control of fractional order chaotic system. The discussion that the stability discrimination of fractional order nonlinear system is converted into that of corresponding integer order nonlinear system has an important significance. In this paper, through the examples, for time-varying coefficient matrix, we point out the existing mistake of the discrimination theorem that states that if the integer system is stable, then its corresponding fractional system with order less than one is also stable. We also analyze the causes of the mistake.%分数阶非线性系统稳定性理论的研究对于分数阶混沌系统同步控制的应用具有重要价值,将分数阶非线性系统稳定性判断转化为相应整数阶非线性系统稳定性判断的探讨很有意义.通过实例表明了:对于时变系数矩阵,如果整数阶系统稳定,其对应的阶次小于1的分数阶系统也稳定的判定定理是错误的,并分析了问题产生的原因.