This paper studies the stability problem of switched systems with state-dependent delayed impulses (SDDIs), where switching times satisfy the definition of average dwell-time. Firstly, the pulse phenomenon of the systems with SDDIs is avoided under some necessary assumptions. Subsequently, the state-dependent delayed impulsive switched systems can be transformed into the corresponding time-dependent ones by using the B-equivalent method. Furthermore, the stability of stable and unstable systems with time-dependent delayed impulses (TDDIs) are analyzed, where the limitation that the impulsive delays are less than the impulsive intervals is relaxed. Based on the equivalence of the original system and the corresponding switched system with TDDIs, some new stability conditions for the switched systems with SDDIs are derived. Finally, the theoretical results are applied to a switched neural network with SDDIs to demonstrate the validity of the results.

中文翻译：

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通过 B 等效方法实现具有状态相关延迟脉冲的开关系统的指数稳定性


本文研究了具有状态相关延迟脉冲 （SDDI） 的开关系统的稳定性问题，其中开关时间满足平均停留时间的定义。首先，在一些必要的假设下避免了具有 SDDI 的系统的脉冲现象。随后，通过使用 B 等效方法，可以将状态依赖的延迟脉冲开关系统转换为相应的时间依赖系统。此外，分析了具有时间依赖性延迟脉冲 （TDDIs） 的稳定和不稳定系统的稳定性，其中脉冲延迟小于脉冲间隔的限制被放宽。基于原始系统和相应的具有 TDDI 的开关系统的等效性，推导出了具有 SDDI 的开关系统的一些新的稳定性条件。最后，将理论结果应用于具有 SDDI 的开关神经网络，以证明结果的有效性。