Outlier-resistant interval observer design for multirate time-delayed systems under the adaptive event-triggered protocols

Abstract

In this paper, an interval observer has been presented for a type of multirate time-delayed systems subject to measurement outliers under the adaptive event-triggered protocol (AETP). First of all, the multirate sampling system is studied to meet the practical requirements. Meanwhile, for relieving the communication burden, an AETP is considered to schedule the measurement information received by the observer. The augmented system is built at a consistent sampling/update rate by using the lifting technique. Moreover, the occurrence of measurement outliers would pose some serious threats to the reliability of the systems. For the addressed issue, an outlier-resistant interval observer is developed by means of saturation function to weaken the impact of the measurement outliers. A sufficient condition is proposed by using the positive system theory and Lyapunov stability theory to ensure that the interval observer is effective and the error system is input-to-state stable. Besides, the gain matrices of the interval observer are obtained by solving a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed interval observer is verified by a numerical simulation.