Global synchronization of time-invariant uncertainty fractional-order neural networks with time delay

This paper considers the global synchronization problem of time-invariant uncertainty fractional-order neural networks with time delay. First, the time-invariant uncertain items are converted into the positive real uncertainties. Then, in order to deal with time delay terms, a novel free-matrix-based fractional-order integral inequality (FMBFII) is proposed by using the fractional-order Leibniz-Newton formula and a new class of Lyapunov-Krasovskii functions is constructed. Next, based on FMBFII, Lyapunov-Krasovskii functions and fractional-order integral Jensen's inequality, several global synchronization criteria for time-invariant uncertainty fractional-order neural networks with time delay are studied. Furthermore, compared to the previous fractional-order integral Jensen's inequality, the advantage of the proposed FMBFII is theoretically analyzed. Finally, by using two examples, the feasibility and effectiveness of our proposed results are tested. (C) 2019 Elsevier B.V. All rights reserved.