An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach

In this brief, we propose a class of generalized memristor-based neural networks with nonlinear coupling. Based on the set-valued mapping theory, novel Lyapunov indefinite derivative and Memristor theory, the coupled memristor-based neural networks (CMNNs) can achieve fixed-time stabilization (FTS) by designing a proper pinning controller, which randomly controls a small number of neuron nodes. Different from the traditional Lyapunov method, this paper uses the implementation method of indefinite derivative to deal with the non-autonomous neural network system with nonlinear coupling topology between different neurons. The system can obtain stabilization in a fixed time and requires fewer conditions. Moreover, the fixed stable setting time estimation of the system is given through a few conditions, which can eliminate the dependence on the initial value. Finally, we give two numerical examples to verify the correctness of our results.