On semi-global exponential stability via observer-based periodic event-triggered controllers

In this paper, the exponential stabilization problem of nonlinear time-delay systems by means of digital periodic event-triggered dynamic output feedback controllers is addressed. In particular, for the class of control-affine nonlinear systems with state delays, a methodology for the design of quantized sampled-data observer-based periodic event-triggered (QSOPE) exponential stabilizers is provided. As a first step, the new notion of Dynamic Output Exponential Descent Feedback (DOEDF) is introduced. Then, the stabilization in the sample-and-hold sense theory and a Halanay’s inequality are suitably combined to prove the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: a proposed digital periodic event-triggered implementation of DOEDFs ensures the semi-global exponential stability of the corresponding closed-loop system. Nonlinear delay-free systems are here addressed as a special case. The proposed results are validated through an application concerning a cascade chemical system with two reactors.