Riccati-Based Design of Event-Triggered Controllers for Linear Systems With Delays

Abstract

In event-triggered control (ETC) systems, the measured state or output of the plant is sent to the controller at so-called event times . In many ETC systems, these event times are generated based on a static function of the current state or output measurement of the system and its sampled-and-held version that is available to the controller. Hence, the event-generator does not include any dynamics of its own. In contrast, dynamic event-generators trigger events based on additional dynamic variables, whose dynamics depend on the state or output of the system. In this paper, we propose new static and dynamic continuous event-generators (which require continuous measuring of the plant output) and periodic event-generators (which only require periodic sampling of the plant output) for linear control systems with communication delays. All event-generators we propose lead to closed-loop systems which are globally exponentially stable with a guaranteed decay rate, $\mathcal L_2$ -stable with a guaranteed $\mathcal L_2$ -gain, and have a guaranteed positive minimum inter-event time. By using new Riccati-based analysis tools tailored to linear systems, the conservatism in our decay rate and $\mathcal L_2$ -gain estimates is small. The dynamic event-generators even further reduce this conservatism, and as a result typically generate significantly fewer events than their static counterparts, while guaranteeing the same control performance. The benefits of these new event-generators are demonstrated via two numerical examples.