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

Abstract

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.