First order approximation of partial exponential stability of nonlinear time-varying systems
非线性时变系统部分指数稳定的一次近似

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.