Design of H∞ control of neural networks with time-varying delays

• Published in: Neural computing & applications Vol. 22; no. Suppl 1; pp. 323 - 331
• Main Authors: Phat, V. N., Trinh, H.
• Format: Journal Article
• Language: English
• Published: London Springer-Verlag 01.05.2013
• Subjects: Artificial Intelligence; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Data Mining and Knowledge Discovery; Image Processing and Computer Vision; Original Article; Probability and Statistics in Computer Science; Time-delay systems; control; Linear matrix inequalities; Neural networks; Stabilization; Lyapunov function
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-012-0820-x

This paper deals with the H ∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov–Krasovskii functionals, we establish new sufficient conditions for H ∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.