A General Approach to Fixed-time Synchronization Problem for Fractional-order Multi-dimension-valued Fuzzy Neural Networks Based on Memristor

In this paper, a general approach to fixed-time synchronization problem is investigated for the general system of fractional-order multi-dimension-valued fuzzy memristive neural networks (FOMDVFMNN). First, we complete the establishment of the new model which is so general that we can regard it as fractional-order real-valued fuzzy memristive neural networks (FORVFMNN), fractional-order complex-valued fuzzy memristive neural networks (FOCVFMNN), and fractional-order quaternion-valued fuzzy memristive neural networks (FOQVFMNN). Then, we mainly apply two new general inequalities such as extended Cauchy-Schwarz inequality and generalized derivative of fractional-order absolute value function in order to realize the general analysis on the discussed problem. Owe to the two new lemmas, we can construct the general Lyapunov-Krasovskii functional (LKF) with adjustable coefficients, design the nonlinear controllers with fuzzy gains as well as acquire the flexible criteria with several useful factors. Particularly, the acquisition of the less conservative fixed time benefits from the new controllers which not only contains the common feedback gains but also contains the general coefficients and the fuzzy gains. Finally, a numerical example is provided to demonstrate our theoretical results.