Stability Analysis for Neural Networks With Time-Varying Delay Based on Quadratic Convex Combination

• Published in: IEEE transaction on neural networks and learning systems Vol. 24; no. 4; pp. 513 - 521
• Main Authors: Zhang, Huaguang, Yang, Feisheng, Liu, Xiaodong, Zhang, Qingling
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Connectionism. Neural networks; Delay; Exact sciences and technology; Linear matrix inequalities; Neural networks; Neural Networks (Computer); Quadratic convex combination; recurrent neural network (RNN); stability analysis; Stability criteria; Symmetric matrices; Time Factors; time-varying delay; Vectors; recurrent neural network (RNN); Recurrent neural nets; time-varying delay; Stability; stability analysis; Lyapunov method; Stability criterion; Neural network; Jensen inequality; Delay; Time varying system; Quadratic convex combination; Efficiency; Linear matrix inequality; Convex function; Delay time; Lyapunov function; Quadratic function
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2012.2236571

In this paper, a novel method is developed for the stability problem of a class of neural networks with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time-varying delay are derived by the newly proposed augmented simple Lyapunov-Krasovski functional. Different from previous results by using the first-order convex combination property, our derivation applies the idea of second-order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to Jensen's inequality. A numerical example is provided to verify the effectiveness and superiority of the presented results.