技术报告：具有基于$\mathcal{L}_2$的事件触发机制的扰动LTI系统的时序抽象
Technical Report: Timing Abstraction of Perturbed LTI systems with $\mathcal{L}_2$-based Event-Triggering Mechanism
AI总结：
本文提出一种框架，用于构建捕获扰动LTI系统采样行为的时序安全自动机，通过基于$\mathcal{L}_2$的事件触发机制，利用稳定性分析技术和时间多面体嵌入，推导出采样间隔的LMI条件，并通过可达性分析确定自动机的转换。
摘要：
在网络控制系统中，事件触发策略在采样过程中的出现导致了网络容量的使用减少，如通信带宽。然而，事件触发策略生成的非周期性采样周期阻碍了此类网络的调度性。本文提出了一种框架，用于构建一个时序安全自动机，以捕获具有基于$\mathcal{L}_2$的触发机制的扰动LTI系统的采样行为。在此框架中，状态空间被划分为有限数量的凸多面体锥体，每个锥体代表抽象自动机中的一个离散模式。采用来自延迟系统稳定性分析的技术，结合时间的多面体嵌入，推导出与每个区域相关的采样间隔的LMI条件。然后，利用可达性分析，推导出抽象自动机的转换。
英文摘要：
In networked control systems, the advent of event-triggering strategies in the sampling process has resulted in the usage reduction of network capacities, such as communication bandwidth. However, the aperiodic nature of sampling periods generated by event-triggering strategies has hindered the schedulability of such networks. In this study, we propose a framework to construct a timed safety automaton that captures the sampling behavior of perturbed LTI systems with an $\mathcal{L}_2$-based triggering mechanisms proposed in the Literature. In this framework, the state-space is partitioned into a finite number of convex polyhedral cones, each cone representing a discrete mode in the abstracted automaton. Adopting techniques from stability analysis of retarded systems accompanied with a polytopic embedding of time, LMI conditions to characterize the sampling interval associated with each region are derived. Then, using reachability analysis, the transitions in the abstracted automaton are derived.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
