On the Digital Event-Triggered Observer-Based Control of Nonlinear Time-Delay Systems

In this letter, the stabilization problem of nonlinear systems with state delays by means of event-triggered observer-based quantized sampled-data controllers is studied. As a first step, the notion of Steepest Descent Feedback, introduced in the context of static state feedbacks controllers, is suitably reformulated to cope with the case of observer-based stabilizers. Then, the stabilization in the sample-and-hold sense is used as a tool to prove the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that the quantized sampled-data event-triggered implementation of SDFs (continuous or not), induced by state observers, ensures the semi-global practical stability property of the related digital closed-loop system with arbitrarily small final target ball of the origin. In the theory here developed, time-varying sampling periods and the non-uniform quantization of both input/output channels are allowed. An application concerning a continuous stirred tank reactor with recycle is studied to show the potential of the approach.