Discrete fixed-time observers over sensor networks with unknown noise

Abstract

This paper investigates fixed-time observers for a class of sensor networks with unknown noise. Specifically, the strongly observable condition and observer matching condition are provided for the convenience of analysis. Two kinds of fixed-time observers for sensor networks are developed based on the system’s observability and the properties of nilpotent matrices. The convergence time of the first kind of observer depends on the target state’s dimension and the rank of the noise input matrix. Besides, to further reduce the convergence time, another kind of observer is designed with the thought of the reduced-order observer. Its convergence time is related to the dimension of the target state and the rank of the augmented measurement matrix. Finally, the effectiveness of the proposed fixed-time observers is demonstrated by simulation examples.