Event-Triggered Control of Nonlinear Systems with Time-Varying State Delays

Nonlinear systems with time delays have been object of intense investigation in the last decades for their ability of capturing the behavior of many natural and engineering systems, including ecological, biomedical, industrial, robotic, and networked systems. In this article, a method for the event-triggered stabilization in the sample-and-hold sense of nonlinear time-delay systems with time-varying state delays is presented. The approach exploits control Lyapunov-Razumikhin functions and a spline-based approximation of the functional state feedback, resulting in a finite-memory controller that avoids (by construction) continuous-state monitoring while ensuring also that the minimal interevent time is strictly positive. Examples of application of the illustrated technique highlight the potential of the approach taken.