H∞ state estimation for delayed neural networks via variable-augmented-based free-weighting matrices method

Abstract

The issue of $H_{\infty }$ state estimation for neural networks with time-varying delays is investigated in this study. Firstly, an augmented Lyapunov-Krasovskii functional (LKF) with two delay-product-type terms is constructed to enhance the consideration of system state, delay, and delay derivative information. Furthermore, for taking into account more effective information, the LKF is augmented with both single and double integral variables. Accordingly, the LKF derivative becomes a higher-order term that exhibits nonlinear characteristics of the time delay. To solve the nonlinear problem, a variable-augmented-based free-weighting-matrices (VAFWMs) approach is employed to transform the nonlinear term into a linear form and provides more freedom in obtaining less-conservative results. Consequently, two improved $H_{\infty }$ state estimation criteria are derived. Lastly, a numerical example is provided to demonstrate the merits and effectiveness of the presented methods. Meanwhile, to prove the practical viability of the presented methods, this study extends the methods to a real-world quadruple-tank process system.