具有记忆的混合系统：广义解的存在性和适定性
Hybrid systems with memory: Existence and well-posedness of generalized solutions
AI总结：
本文研究具有记忆的混合系统，通过广义解的概念建立框架，证明在混合数据的正则性条件下，广义解的存在性，并利用图形收敛拓扑证明系统适定性，进而展示其预渐近稳定性。
摘要：
具有记忆的混合系统是指表现出混合和延迟现象的动态系统。尽管此类系统在许多物理和工程系统中常见，特别是在控制应用中，围绕混合延迟系统鲁棒性的各种问题尚未得到充分解决。本文在允许通过广义解概念研究混合系统记忆的框架下，建立了一些基本结果。特别地，我们通过在混合轨迹相空间中配备图形收敛拓扑的正则性条件，开发了广义解的基本存在性。与通常使用的统一收敛拓扑不同，采用图形收敛拓扑使我们能够建立具有记忆的混合系统的适定性。我们然后展示，由于适定性，预渐近稳定的适定混合系统具有记忆的鲁棒性。
英文摘要：
Hybrid systems with memory refer to dynamical systems exhibiting both hybrid and delay phenomena. While systems of this type are frequently encountered in many physical and engineering systems, particularly in control applications, various issues centered around the robustness of hybrid delay systems have not been adequately dealt with. In this paper, we establish some basic results on a framework that allows to study hybrid systems with memory through generalized concepts of solutions. In particular, we develop the basic existence of generalized solutions using regularity conditions on the hybrid data, which are formulated in a phase space of hybrid trajectories equipped with the graphical convergence topology. In contrast with the uniform convergence topology that has been often used, adopting the graphical convergence topology allows us to establish well-posedness of hybrid systems with memory. We then show that, as a consequence of well-posedness, pre-asymptotic stability of well-posed hybrid systems with memory is robust.
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