Nonfragile<i>H</i><sub>∞</sub>State Estimation for Recurrent Neural Networks With Time-Varying Delays: On Proportional–Integral Observer Design
Di Zhao, Zidong Wang, Guoliang Wei, Xiaohui Liu
Abstract
In this article, a novel proportional–integral observer (PIO) design approach is proposed for the nonfragile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> state estimation problem for a class of discrete-time recurrent neural networks with time-varying delays. The developed PIO is equipped with more design freedom leading to better steady-state accuracy compared with the conventional Luenberger observer. The phenomena of randomly occurring gain variations, which are characterized by the Bernoulli distributed random variables with certain probabilities, are taken into consideration in the implementation of the addressed PIO. Attention is focused on the design of a nonfragile PIO such that the error dynamics of the state estimation is exponentially stable in a mean-square sense, and the prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance index is also achieved. Sufficient conditions for the existence of the desired PIO are established by virtue of the Lyapunov–Krasovskii functional approach and the matrix inequality technique. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed PIO design scheme.