Abstract This article employs the hybrid-system-with-memory formalism to attain transmission intervals and delays that provably stabilize Networked Control Systems (NCSs). Nonlinear time-varying plants and controllers with variable discrete and distributed input, output and state delays along with nonconstant discrete and distributed network delays are considered. We bring together nominal system L 2 -stability, Uniformly Globally Exponentially Stable (UGES) scheduling protocols and linear upper bounds of network-induced output error dynamics to infer Uniform Global pre-Asymptotic Stability (UGpAS) of the closed-loop system via Lyapunov–Krasovskii arguments. Namely, we replace the Lyapunov–Razumikhin conditions and trajectory-based small-gain theorem with linear L 2 -gains arguments, featured in our previous works, with Lyapunov–Krasovskii functionals to prove UGpAS of interconnected hybrid systems with memory. The present methodology allows for more general delays (e.g., multiple input/output/state discrete and distributed delays) and output error dynamics (e.g., multiple discrete and distributed delays) as well as less conservative estimates of Maximally Allowable Transfer Intervals (MATIs). Our results are applicable to control problems with output feedback and the so-called large delays, that is, delays larger than the transmission intervals. In addition, model-based estimators between two consecutive updates, rather than merely the Zero-Order Hold (ZOH) strategy, are allowed for in order to prolong MATIs. Lastly, a nonlinear numerical example involving a single-link robot arm and observer–predictor-based control law is provided to illustrate our theoretical findings.

中文翻译：

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通过具有记忆的混合系统建模和 Lyapunov-Krasovskii 参数稳定非线性网络控制系统中的传输间隔和延迟

摘要 本文采用具有内存的混合系统形式来获得可证明稳定网络控制系统 (NCS) 的传输间隔和延迟。考虑了具有可变离散和分布式输入、输出和状态延迟以及非恒定离散和分布式网络延迟的非线性时变设备和控制器。我们将标称系统 L 2 稳定性、均匀全局指数稳定 (UGES) 调度协议和网络引起的输出误差动态的线性上限结合起来，通过 Lyapunov– 推断闭环系统的均匀全局预渐近稳定性 (UGpAS)–克拉索夫斯基的论点。也就是说，我们用线性 L 2 增益参数替换了 Lyapunov-Razumikhin 条件和基于轨迹的小增益定理，这在我们之前的工作中是有特色的，使用 Lyapunov-Krasovskii 泛函证明具有内存的互连混合系统的 UGpAS。本方法允许更一般的延迟（例如，多个输入/输出/状态离散和分布式延迟）和输出误差动态（例如，多个离散和分布式延迟）以及最大允许传输间隔（MATIs）的不太保守的估计。我们的结果适用于具有输出反馈和所谓大延迟（即大于传输间隔的延迟）的控制问题。此外，允许在两次连续更新之间使用基于模型的估计器，而不仅仅是零阶保持 (ZOH) 策略，以延长 MATI。最后，