Input-to-state stability of event-based state-feedback control

This paper investigates the stability of event-based state-feedback loops. Two analysis methods are proposed. The first method proves the event-based state-feedback loop to be input-to-state practically stable which means that the state converges to a vicinity of the origin. The size of this region depends upon the magnitude of the disturbance and the event threshold, which is a design parameter. The second method is tailored for event-based state-feedback loops with stable plant dynamics and it shows that the investigated system is input-to-state stable, which implies that for small disturbance magnitudes the size of the region to which the state converges is independent of the event threshold. This new result shows that asymptotic stability can be achieved by means of an event-based controller with constant event threshold which has been proven in literature only for decreasing event thresholds. Both analysis methods are applied to a benchmark example and the results are compared with an analysis method known from literature which shows that the second proposed analysis method yields less conservative results with respect to the ultimate bound than existing methods in literature.