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Stabilizing Transmission Intervals and Delays in Nonlinear Networked Control Systems through Hybrid-System-with-Memory Modeling and Lyapunov-Krasovskii Arguments

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 L2-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 L2-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.

hybrid systems with memory ; Lyapunov methods ; stability of hybrid systems ; networked control systems

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