Abstract

This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

中文翻译：

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基于基本解的无限时滞非瞬时脉冲半线性测量驱动控制系统的近似可控性

摘要

本文研究了一类具有无限延迟的新型非瞬时脉冲测量驱动控制系统。所考虑的系统涵盖了一大类混合系统，对其 Zeno 行为没有任何限制。与普通脉冲微分方程相比，测度微分方程的概念更一般；因此，讨论的结果比现有的结果更普遍。特别是，利用基本解、Krasnoselskii 不动点定理和 Lebesgue-Stieltjes 积分理论，构造了一组新的充分条件，以确保解的存在和所考虑系统的近似可控性。最后，构建了一个例子来证明所得结果的有效性。