The $$l_2-l_{\infty }$$ filtering problem is studied for a class of discrete-time switched systems under the admissible edge-dependent average dwell time (AED-ADT) switching. Firstly, a new multiple convex Lyapunov function (MCLF) is established as a convex combination form in the context of the $$l_2-l_{\infty }$$ filtering problem. Then, corresponding to the MCLF, the quasi-time-dependent switched filter is proposed for the considered switched system, and the sufficient conditions are derived to ensure that the filtering error system is globally uniformly exponentially stable with a prescribed $$l_2-l_{\infty }$$ performance index. Owing to the quasi-time-dependent and multi-degree-of-freedom properties of the designed switched filter, the wider feasibility regions of system parameters, more desirable $$l_2-l_{\infty }$$ disturbance attenuation levels and tighter bounds on the AED-ADT can be acquired. Finally, a numerical example is given to expound that our approach outperforms the extant results.

中文翻译：

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准时间相关 $$l_2-l_\infty $$l2-l∞ 具有可容许边缘相关平均停留时间的离散时间交换系统的滤波

$$l_2-l_{\infty }$$ 过滤问题是针对一类离散时间切换系统在容许边缘相关平均驻留时间（AED-ADT）切换下进行研究的。首先，在$$l_2-l_{\infty }$$过滤问题的上下文中，建立了一个新的多重凸Lyapunov函数（MCLF）作为凸组合形式。然后，对应于MCLF，针对所考虑的切换系统提出了准时间相关切换滤波器，并推导出充分条件以保证滤波误差系统全局一致指数稳定且具有规定的$$l_2-l_{ \infty }$$ 性能指标。由于所设计的开关滤波器具有准时间相关和多自由度的特性，系统参数的可行性范围更广，可以获得更理想的 $$l_2-l_{\infty }$$ 干扰衰减水平和更严格的 AED-ADT 界限。最后，给出了一个数值例子来说明我们的方法优于现有结果。