Novel Adaptive Control and State-Feedback Control Strategies to Finite-Time Stabilization of Discontinuous Delayed Networks

This paper is concerned with the finite-time stabilization problem for a class of delayed neural networks (DNNs) with discontinuous neuron activations. In order to stabilize the states of such DNNs in finite time, we design two classes of novel control strategies including switching adaptive control strategy and switching state-feedback control strategy. Based on the theory of differential inclusions, the famous finite-time stability theorem and the generalized Lyapunov functional method, several sufficient conditions are established to ensure the finite-time stabilization control of discontinuous DNNs. In addition, we also provide the settling time for stabilization which has an important significance in the application of neural networks for guaranteeing fast response. Finally, numerical examples are given to demonstrate the effectiveness of the proposed control strategies and main results.