Outlier-Resistant Nonfragile Control of T–S Fuzzy Neural Networks With Reaction–Diffusion Terms and Its Application in Image Secure Communication

Abstract

This paper focuses on a new outlier-resistant non-fragile control issue for a class of Takagi-Sugeno (T-S) fuzzy delayed neural networks with reaction-diffusion terms (TFRDNNs). Compared with the existing delayed neural networks (DNNs), fuzzy control rules and reaction-diffusion phenomenon are considered simultaneously, which makes the proposed models more practical. Furthermore, when subjected to abnormal interference, measurement outputs result in measurement outliers. In order to mitigate the negative effects on estimation error, a state estimator scheme is presented by introducing a saturation function. By using an appropriate Lyapunov-Krasovskii functional (LKF) and with the help of a free weighting matrix, sufficient conditions can be deduced to guarantee the asymptotical stability and prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance index of the disturbance attenuation of estimation error. Next, a design strategy of outlier-resistant non-fragile state estimator (ONSE) is put forward by employing some decoupling techniques. An illustrative example is exploited to illustrate the validity and feasibility of the proposed state estimator. Finally, the obtained theoretical results are applied to image encryption. The experimental analysis demonstrates that the presented encryption scheme is feasible and effective.