H∞ control for neural networks with discontinuous activations and nonlinear external disturbance

This paper studies the H∞ control problem for a class of neural networks with discontinuous activations and nonlinear external disturbance. Firstly, under the framework of Filippov solution, we investigate the existence of the solution for the discontinuous perturbation neural networks. Secondly, we design linear state feedback controllers and adaptive controllers to ensure the stabilization of the discontinuous neural networks with a generalized H∞ disturbance attenuation level ρ. Finally, we give two examples to show the effectiveness of the designed controllers and the correction of the theoretical results.