具依赖状态脉冲的积分微分系统的实际稳定性

Practical Stability for Impulsive Integro-differertial Equations with Variable Times

比较方法是研究微分系统解的稳定性的一种基本方法,其优越性在于可利用稳定性相对易解决的比较系统的稳定性质得到给定较复杂微分系统的相应稳定性结果;而锥值Lyapunov函数方法可以减弱比较系统的拟单调非减性要求。将这两种方法相结合,通过与常微分系统作比较,利用锥值Lyapunov函数与微分不等式建立了具依赖状态脉冲积分微分系统新的比较原理,此比较原理允许解曲线碰撞同一脉冲面有限次。在此基础上给出此类系统的实际稳定性的比较结果。

Comparison method is a basic method to study the stability of the solution of differential system,and its superiority lies in getting the corresponding stability result of a given complicated differential system by the stability of the comparison system whose stability is relatively easy to solve.The method of cone-valued Lyapunov function can weaken the requirement of quasimonotone nondecreasing property of the comparison system.These two kinds of methods are combined.And a new comparison principle of impulsive integro-differential equations with variable times is established by employing cone-valued Lyapunov function and differential inequality through comparing with the ordinary differential equations.The comparison principle allows trajectories strike the same hypersurface finint time,and then be applied to obtain a practical stability criterion of such systems.