On H∞ Fuzzy Proportional-Integral Observer Design Under Amplify-and-Forward Relays and Multirate Measurements

In this article, we investigate the so-called
$H_{\infty }$
fuzzy proportional-integral observer (PIO) design problem for a class of nonlinear systems subject to relay effects, data missing, and multirate measurements. The considered multirate phenomenon is defined as the employment of sensors with diverse sampling periods due to specific engineering requirements. During the long transmission from multirate sensors to the remote fuzzy observer, the amplify-and-forward relay scheme is utilized to facilitate data communication, in which the measurement outputs are first directed to the relay nodes and then sent to the observer side. A unified model, incorporating both fast and slow sampling, is described using the switching system method. Subsequently, a fuzzy PIO is proposed by utilizing estimated premise variables along with current and historical system information. Through the application of stochastic analysis theory, the error dynamics of the state estimation is examined, and the observer gain matrices are determined by solving a specific convex optimization problem. Ultimately, two simulation experiments are conducted to validate the efficacy and utility of the formulated fuzzy PIO.