Absolute stabilization of Lur'e systems under event-triggered feedback

Abstract

In this paper, we deal with event-triggered feedback control for Lur'e systems that consist of negative feedback interconnection of nominal linear dynamics and an unknown static nonlinearity. The unknown nonlinearity is conventionally assumed to lie in a given sector while the sector bounds are known. In the presence of event-triggered feedback mechanisms, the control input is only computed and updated when a specific event occurs. In this sense, control system resources (e.g. computation and communication capabilities) can be saved. A sufficient condition for the existence of an event-triggering condition and the corresponding even-triggered controller design are obtained by means of linear matrix inequality techniques. In addition, the avoidance of Zeno behavior is guaranteed. Furthermore, a result on the event-triggered emulation of a continuous-time feedback controller for Lur'e systems is presented. Finally, numerical simulations are given to illustrate the theoretical results along with some concluding remarks.