Sampled-data event-triggered control with sampling-independent positive guarantees on inter-event times

To fit with a digital environment in networked control systems, sampled-data event-triggered control (ETC) has been proposed where the event-triggering mechanisms sense and process information only at discrete sampling instants (not necessarily periodically). One deficiency in the previous study on sampled-data ETC is the lack of analysis on transmission performance, which yields the potential occurrence of an undesirable phenomenon that the minimum inter-event time is always equal to the minimum inter-sampling interval, no matter how small the latter is. To overcome this drawback, in this paper, we propose a novel sampled-data ETC scheme such that the lower bounds of inter-event times have sampling-independent positive guarantees. A linear networked control system is considered under observer-based controllers, external disturbances, and multiple communication channels. The improved transmission performance is due to the utilization of dynamic event-triggering conditions and some mean-rate error signals, which are the ratios between network-induced errors and some time-increasing functions. After modeling the closed-loop dynamics into a hybrid system, sufficient conditions on the upper bound of inter-sampling intervals and parameters in ETC are provided to ensure input-to-state stability (rather than its practical version) and sampling-independent positive guarantees simultaneously. Furthermore, a new tradeoff relationship between the sampling and transmission performance is revealed: a faster sampling frequency is conducive to improving inter-event times. Finally, a linearized model of an inverted pendulum is simulated to illustrate the efficiency and feasibility of the obtained results.