Vector Wirtinger-type inequality and the stability analysis of delayed neural network

This paper proposes some new stability criteria for a class of delayed neural networks with sector and slope restricted nonlinear neuron activation function. By using the convex express of the nonlinear neuron activation function, the original delayed neural network is transformed into a linear uncertain system. The proposed method employs an improved vector Wirtinger-type inequality for constructing a novel Lyapunov functional. Based on the Lyapunov stable theory, new delay-dependent and delay-independent stability criteria for the researched system are established in terms of linear matrix inequality technique, delay partitioning approach and characteristic root method. Three illustrative examples are presented to verify the effectiveness of the main results.

► We transform nonlinear system into an uncertain linear system by using convex method.
► We establish a new vector Wirtinger-type inequality to derive stability criteria.
► A novel piecewise-convex Lyapunov functional is constructed.
► A method to calculate the upper bound of the activation function is provided.