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Controllers are often designed based on a reduced or simplified model of theplant dynamics. In this context, we investigate whether it is possible tosynthesize a stabilizing event-triggered feedback law for networked controlsystems (NCS) which have two time-scales, based only on an approximate model ofthe slow dynamics. We follow an emulation-like approach as we assume that weknow how to solve the problem in the absence of sampling and then we study howto design the event-triggering rule under communication constraints. The NCS ismodeled as a hybrid singularly perturbed system which exhibits the feature togenerate jumps for both the fast variable and the error variable induced by thesampling. The first conclusion is that a triggering law which guarantees thestability and the existence of a uniform minimum amount of time between twotransmissions for the slow model may not ensure the existence of such a timefor the overall system, which makes the controller not implementable inpractice. The objective of this contribution is twofold. We first show thatexisting event-triggering conditions can be adapted to singularly perturbedsystems and semiglobal practical stability can be ensured in this case. Second,we propose another technique that combines event-triggered and time-triggeredresults in the sense that transmissions are only allowed after a predefinedamount of time has elapsed since the last transmission. This technique has theadvantage, under an additional assumption, to ensure a global asymptoticstability property and to allow the user to directly tune the minimuminter-transmission interval. We believe that this technique is of its owninterest independently of the two-time scale nature of the addressed problem.The results are shown to be applicable to a class of globally Lipschitzsystems.

Event-triggered control of nonlinear singularly perturbed systems based only on the slow dynamics