In this paper, the asynchronous $l_2-l_{\mathrm{\infty }}$ filtering problem is directed at a kind of discrete-time impulsive switched systems, where ‘asynchronous’ implies that there is a delay when switching occurs between filter modes and system modes. A novel Lyapunov function has been constructed. The inventiveness lies in discontinuity of Lyapunov-like function at both the switching time and the instant when the system modes and filter modes are matched. An improved inequality portraying the relationship among Lyapunov-like function, impulse, asynchronous phenomena and disturbance is built to pledge the $l_2-l_{\mathrm{\infty }}$ performance. On the basis of directed graph, the novel Lyapunov function, the improved inequality and admissible edge-dependent average dwell time technology, some criteria suitable for proving the globally uniformly exponential stability of filtering error system are proposed with $l_2-l_{\mathrm{\infty }}$ performance index, and the relevant filter can also be designed. Finally, three numerical examples show the availability of the obtained conclusions.

本文中，异步 ${升}_2-{升}_{\mathrm{\infty }}$滤波问题针对一种离散时间脉冲切换系统，其中“异步”表示在滤波器模式和系统模式之间进行切换时存在延迟。构造了一个新颖的Lyapunov函数。本发明的发明之处在于，在切换时间以及系统模式和滤波器模式匹配的瞬间，都具有类Lyapunov函数的不连续性。描述了类Lyapunov函数，脉冲，异步现象和干扰之间关系的改进不等式，以保证${升}_2-{升}_{\mathrm{\infty }}$性能。在有向图的基础上，提出了新颖的李雅普诺夫函数，改进的不等式和允许的边沿相关平均停留时间技术，提出了一些适合证明滤波误差系统的全局一致指数稳定性的准则，其中${升}_2-{升}_{\mathrm{\infty }}$性能指标，还可以设计相关的滤波器。最后，三个数值例子说明了所得结论的有效性。