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

Abstract

This article focuses on a new outlier-resistant nonfragile control issue for a class of Takagi–Sugeno fuzzy delayed neural networks with reaction–diffusion terms. Compared with the existing delayed neural networks, 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 the estimation error, a state estimator scheme is presented by introducing a saturation function. By using an appropriate Lyapunov–Krasovskii functional 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 the estimation error. Next, a design strategy of an outlier-resistant nonfragile state estimator 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.