Adaptive event-triggered control for uncertain linear systems with process time-varying delays

Abstract

This paper concerns an event-triggered control for uncertain linear systems with process time-varying delays. An adaptive event trigger (AET) is employed for reducing the data transmission amount from the sensor to the controller. Because a positive constant and a positive variable are simultaneously involved in the AET, the AET condition may be difficult to be violated and the data transmission amount may be reduced. A discrete-time feedback control law is employed to guarantee the uniformly ultimately bounded (UUB) of the closed-loop systems. If the gain matrix of the time-delayed state is compromised with the sufficient stability condition, the desired stability can be always achieved regardless of the time-varying delays. In addition, the bound region can be specified by regulating the threshold of the AET. It is proved that the unwanted Zeno phenomena is naturally excluded since the minimal event-triggered time-interval of the AET is a positive real number. Furthermore, the maximal event-triggered time interval can also be quantitatively approximated. A numerical example is provided to demonstrate the effectiveness of the proposed method, and the influences of the AET threshold and time delay are discussed as well.