时标上脉冲动态系统的指数稳定性

Exponential Stability of Impulsive Dynamic Systems on Time Scales

利用Lyapunov函数直接方法研究了时标上固定时刻脉冲动态系统的指数稳定性,并给出了此系统指数稳定性的几个判别准则。由于时标理论是离散和连续的统一,时标上脉冲动态系统的稳定性研究更具有普遍性,它包含了已有的脉冲微分系统指数稳定性的结果。同时,给出的定理中对Lyapunov函数的Δ-导数及其在脉冲点处的要求更具一般性,使得定理具有更广泛的适用范围。最后给出了一个例子说明其应用。

The exponential stability of impulsive dynamic systems with fixed impulse on time scales by using Lyapunov function direct method is investigated,and obtained some criterias of exponential stability for the system.Since the scale theory can unify the continuous theory and discrete theory,which is on impulse dynamic systems on time scales is more universal and it obtains the previous exponential stability results of impulse differential system.Also,the requirement of the Δ-derivative and its property at impulse is more common.So the scope of application of the theory is wider.In the end,an example is given to illustrate the application of the result.