Stability (learning theory)

Mathematics

Mathematical optimization

Regular polygon

Machine learning

Mathematical analysis

Artificial intelligence

Linear matrix inequality

Geometry

Computer science

Inequality

Applied mathematics

Artificial neural network

IEEE Transactions on Neural Networks and Learning Systems

This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.

Stability Analysis for Delayed Neural Networks via a Generalized Reciprocally Convex Inequality