Asymptotic Stability and Synchronization of Fractional Delayed Memristive Neural Networks with Algebraic Constraints

In this paper, we investigate the global asymptotic stability and synchronization of fractional delayed memristive neural networks with algebraic constraints in sense of Riemann-Liouville. Firstly, inspired by the existing neural network models with constraints, we use fractional singular delayed systems to model a new class of fractional delayed memristive neural networks with algebraic constraints, namely, fractional singular delayed memristive neural networks. Next, within the framework of Filippov’s solution, a less conservative criterion for the asymptotic stability of fractional singular delayed memristive neural networks is given by endowing Lyapunov direct method. Then, the appropriate feedback controllers and adaptive controllers are designed to realize the synchronization of the fractional singular delayed memristive neural networks and two sufficient conditions for global asymptotic synchronization are obtained. In addition, the above results not only address the effects of time delays and algebraic constraints, but also can easily detect and synchronize the actual memristive neural networks. Finally, three numerical examples are elaborated to verify the correctness and validity of theoretical results