Sampled-data and event-triggered control of globally Lipschitz infinite-dimensional systems
Rami Katz, Andrii Mironchenko
TL;DR
This work develops a general framework for stabilizing linear infinite-dimensional systems via sampled-data and event-triggered control when stabilization is achievable by compact feedback and the nonlinearity through a globally Lipschitz map satisfies a small sector bound. It proves that a zero-order-hold sampled-data controller $u(t)=F x(k\\tau)$ stabilizes the closed-loop for small $\\tau$ and $\\theta_f$, and it extends to a switching-based event-triggered scheme based on an ISS Lyapunov function $V$, yielding UGAS under a non-Zeno updating rule. The main technical contribution is a sufficient recursion-based criterion ensuring stability of the ET-controlled system, supported by a dissipation analysis and a demonstration on a Sturm–Liouville parabolic PDE, where a finite-dimensional unstable block can be stabilized by a compact feedback and thus stabilizes the full system. This framework advances resource-efficient stabilization of distributed-parameter systems with Lipschitz nonlinearities and bounded input operators, with potential extensions to unbounded inputs and full ET analysis. The practical impact lies in enabling robust, low-update-rate control of PDE-like dynamics in applications where compact feedback is feasible.
Abstract
We show that if a linear infinite-dimensional system is exponentially stabilizable by compact feedback, it is also stabilizable by means of a sampled-data feedback that is fed through a globally Lipschitz nonlinearity, provided that the sector bound for the nonlinearity and the sampling time is small enough. Next we develop a switching-based event-triggered control scheme stabilizing the system with a reduced number of switching events. We demonstrate our results on an example of finite-dimensional stabilization of a Sturm-Liouville parabolic system.