非线性时变系统部分指数稳定的一次近似

First order approximation of partial exponential stability of nonlinear time-varying systems

通过非线性系统的线性化方法,讨论了一类非线性时变微分系统的解关于部分变量指数稳定的一次近似.利用齐次线性系统的Cauchy矩阵解、截断Cauchy矩阵解和Gronwall_Bellman不等式,得到了线性系统的解部分指数稳定确保原非线性系统的解局部部分指数稳定的充分条件,其中一些结果可以保证部分变量有不同的指数收敛率.最后给出了一些实例说明了所用方法的有效性.

The first order approximation of the partial exponential stability of nonlinear time-varying systems is investigated by linearization approach of nonlinear systems. Based on Cauchy matrices solutions and its interceptive Cauchy matrices solutions of homogeneous linear systems, as well as the Gronwall-Bellman inequality, some sufficient conditions of partial exponential stability are obtained for the systems and some of these results are proved to be able to guarantee different exponential convergence for partial solutions of the systems. Finally, two numerical examples are presented to verify the effectiveness of proposed approach.