Dynamical analysis of uncertain neural networks with multiple time delays

Abstract

This paper investigates the robust stability problem for dynamical neural networks in the presence of time delays and norm-bounded parameter uncertainties with respect to the class of non-decreasing, non-linear activation functions. By employing the Lyapunov stability and homeomorphism mapping theorems together, a new delay-independent sufficient condition is obtained for the existence, uniqueness and global asymptotic stability of the equilibrium point for the delayed uncertain neural networks. The condition obtained for robust stability establishes a matrix–norm relationship between the network parameters of the neural system, which can be easily verified by using properties of the class of the positive definite matrices. Some constructive numerical examples are presented to show the applicability of the obtained result and its advantages over the previously published corresponding literature results.

Keywords:

• robust stability
• neural networks
• uncertain systems
• time delays

Additional information

Notes on contributors

Sabri Arik

Sabri Arik received the Dipl Ing degree from Istanbul Technical University, Istanbul, Turkey, the PhD degree from the London South Bank University, London, UK, and the Habilitation degree from Istanbul University, Istanbul, Turkey. He is working as a full professor at the Department of Computer Engineering, Istanbul University. He is on leave from Istanbul University since 2011, and currently serving as the dean of Faculty of Art and Science of Isik University, Istanbul, Turkey. His major research interests include cellular neural networks, non-linear systems and matrix theory. He has authored and co-authored some 50 publications. Dr Arik is a member of the IEEE Circuits and Systems Society Technical Committee of Cellular Neural Networks and Array Computing. He is also a board member of Asia Pacific Neural Network Assembly. He was the recipient of the Outstanding Young Scientist Award in 2002 from the Turkish Academy of Sciences, Junior Science Award in 2005 from the Scientific and Technological Research Council of Turkey and the Frank May Prize (Best Paper Award) in 1996 from the London South Bank University. He also serves as the associate editor for journals Neurocomputing, Neural Processing Letters and International Journal of Differential Equations.