Dynamic event-triggered control with time regularization for linear systems

We present a framework for the analysis and design of dynamic and static event-triggered controllers with time regularization for linear systems. This framework leads to guarantees on global exponential stability, ℒ ₂ -stability, and a positive minimum inter-event time, in addition to a reduction in the number of events compared to regular time-triggered controllers and other event-triggered controllers in literature. By using new analysis tools tailored to linear systems, we achieve a significant reduction in conservatism, in the sense that the novel framework yields new event-generator designs with much larger inter-event times and much tighter bounds on the ℒ ₂ -gain and convergence rate of the event-triggered control system compared to previous results for more general nonlinear systems. We demonstrate the benefits of our new results via a numerical example, and show that the conservatism in the estimates of the ℒ ₂ -gain is indeed small.