Asymptotic stability and synchronization of fractional delayed memristive neural networks with algebraic constraints.

The asymptotic stability and synchronization of fractional delayed memristive neural networks with algebraic constraints in Riemann–Liouville sense will be investigated in this article. First, algebraic constraints are introduced for the first time into the existing fractional delayed memristive neural networks, and a new fractional singular delayed memristive neural networks (FSDMNNs) model is presented. Then, within the framework of Filippov's solution, a less conservative result for the asymptotic stability of FSDMNNs is obtained by Lyapunov–Krasovskii functional. Subsequently, the appropriate feedback scheme and adaptive scheme are designed to synchronize FSDMNNs and two sufficient conditions are acquired. In addition, the results not only address the influence of delays and algebraic constraints, but can also easily detect and synchronize the actual memristive neural networks. Finally, numerical simulations frankly confirm the correctness and validity of the derived results. • This paper considers the influence of algebraic constraints on FDMNNs. • A new stability criterion of FSDMNNs is attained by a novel Lyapunov functional. • Two easy-to-verify synchronization conditions are gained by suitable controllers. • Our results can be deemed an extension of the existing ones. [ABSTRACT FROM AUTHOR]