PeriodicEvent-TriggeredControl forNetworkedControl SystemsBased onNon-Monotonic LyapunovFunctions ?

This article considers exponential stabilization of linear Networked Control Systems with periodic event-triggered control for a given network specification in terms of a maximum number of successive dropouts and a constant transmission delay. Based on stability results using non-monotonic Lyapunov functions for discontinuous dynamical systems, two sufficient results for stability of the general model of a linear event-triggered Networked Control System are derived. Those results are used to derive robust periodic event-triggered control strategies. First, a static triggering mechanism for the case without delay is derived. Afterwards, two dynamic triggering mechanisms are developed for the case without and with delay. It is shown how a degree of freedom, being contained in the dynamic triggering mechanisms, can be used to shape the resulting network traffic. The applied adaption technique is motivated by existing congestion control mechanisms in communication networks. The properties of the derived mechanisms are illustrated in a numerical example.

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