Chetaev型实用不稳定性判据

利用 Ｖ函数方法研究非线性系统的实用不稳定性。根据Ｃｈｅｔａｅｖ不稳定性定理的基本思想,结合对过初始状态集合边界特解的性态分析,建立了一般形式的实用不稳定性直接判据。此结果能够有效地用于分析非线性系统的实用不稳定性,避免了因使用比较方法使所得条件过强和不便于实际检验的困难,并举例说明所得结果。

Chetaev -like criteria for practical instability

The problem of practical instability of nonlinear systems is considered by means of the V-function method. According to the fundamental idea of Chetaev's instability theorem, general direct criteria for the practical instability of nonlinear systems are established via analyzing the special features of solutions passing through the points on the boundary of the set of initial states. These results can effectively aviod the shortcomings and inconvinences such as so strong conditions that result in a totally practical instability and/or too cumbersome conditions to be handled, etc, encountered in the existing results derived mainly by the so-called "comparison method ". An illustrative example is given to demonstrate the availability of the presently proposed results.