脉冲微分系统关于部分变元的强稳定性

Strong Stability with Respect to Part of the Variables in Systems with Impulse Effect

介绍了一种新的稳定性———脉冲微分系统的解关于部分变元的强稳定性 ,并进而讨论了该类稳定性问题 .首先建立了两个重要的引理 ,然后再借助于逐段连续的Lyapunov函数 ,得到了脉冲微分系统的零解关于部分变元强稳定性的一些判定定理 .

The present paper introduces a new kind of stability——strong stability with respect to part of the variables in systems with impulse effect. The question on the stability is discussed. Effective sufficient conditions are found for strong stability with respect to partial variables of the zero solution of an impulsive differential system. The approach present is based on the specially introduced piecewise continuous Lyapunov functions and two important lemmas. Finally the obtained criteria are applied to the investigation of strong stability of the zero solutions with respect to part of the variables in impulsive differential systems.