An event‐triggered method to distributed filtering for nonlinear multi‐rate systems with random transmission delays

Summary In this article, an event‐triggered recursive filtering problem is studied for a class of nonlinear multi‐rate systems (MRSs) with random transmission delays (RTDs). The RTDs are described by utilizing random variables with a known probability distribution and the Kronecker function. To facilitate further study, the MRS is converted into a single‐rate one by adopting an iteration equation approach. To address the challenge of filter design caused by different measurement sampling periods, a modified prediction method of measurements is given. Moreover, an event‐triggered mechanism (ETM) is introduced to regulate the innovation transmission frequency. The objective of the addressed filtering problem is to design a recursive distributed filtering method for MRSs subject to ETM and RTDs, where a minimum upper bound on the filter error covariance is obtained. Moreover, the filter gain matrix is formulated by resorting to the solutions to matrix difference equations. Besides, the boundedness in the mean‐square sense of the filtering error is analyzed and a sufficient condition is provided. Finally, simulations with comparison experiments are presented to demonstrate the effectiveness of the newly proposed theoretical results.