This paper presents a new approach for analyzing delay-dependent stability and hybrid $L_2\times l_2$-gain performance of linear impulsive delay systems. The new approach is inspired by the delay-partitioning method, the timer-dependent Lyapunov functional method, and the looped-functional method. In the delay-partitioning framework, a new type of timer-dependent Lyapunov functional is constructed, which depends on the partition on impulse intervals and also on impulse dynamics. Different from the previous discontinuous Lyapunov functionals, the introduced Lyapunov functional is continuous along the trajectories of the considered impulsive delay system. Consequently, two different problems of exponential stability and hybrid $L_2\times l_2$-gain performance are tackled by using the same class of Lyapunov functionals. It is shown that the positive definiteness of this Lyapunov functional inside impulse intervals is not necessary for proving exponential stability. By use of new integral inequalities based techniques, delay-dependent criteria for exponential stability and finite hybrid $L_2\times l_2$-gain are established in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach.

本文提出了一种新的方法来分析时滞相关的稳定性和混合 ${\mathrm{大号}}_2\times {升}_2$-线性脉冲延迟系统的性能。这种新方法的灵感来自于延迟分配方法，依赖于计时器的Lyapunov函数方法以及循环函数方法。在延迟划分框架中，构造了一种新型的依赖计时器的Lyapunov函数，该函数依赖于脉冲间隔的划分以及脉冲动力学。与以前的不连续Lyapunov函数不同，引入的Lyapunov函数沿考虑的脉冲时滞系统的轨迹是连续的。因此，存在两个不同的指数稳定性和混合性问题${\mathrm{大号}}_2\times {升}_2$使用相同类别的Lyapunov功能可解决-gain性能。结果表明，该Lyapunov函数在脉冲间隔内的正定性对于证明指数稳定性不是必需的。通过使用新的基于积分不等式的技术，指数稳定性和有限混合的时滞相关准则${\mathrm{大号}}_2\times {升}_2$-增益是根据线性矩阵不等式建立的。提供了数值示例来说明新方法的效率。