Fixed-time synchronization criteria of fuzzy inertial neural networks via Lyapunov functions with indefinite derivatives and its application to image encryption

In this paper, we investigate the fixed-time synchronization for fuzzy inertial neural networks with time-varying coefficients and time delays. The fuzzy inertial neural networks are transformed into two forms of first-order differential systems, and then two kinds of different controllers of time-variable are designed. In these schemes, a series of novel criteria are proposed to ensure the fixed-time synchronization for the drive-response fuzzy inertial neural networks via state feedback control methods. Sufficient conditions of delay-dependent and delay-independent are obtained in terms of algebraic inequalities, not the matrix inequalities. Moreover, these new criteria allow the derivative of the Lyapunov function can be positive, but not negative definite as the earlier work. And the algebraic conditions become easy to be tested under the new criteria. Finally, two examples are added to illustrate effectiveness of the results we obtained. Meanwhile, a new image encryption algorithm is proposed based on the synchronization of drive-response networks, and the effectiveness of this algorithm is also demonstrated. (c) 2022 Elsevier B.V. All rights reserved.