×

Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. (English) Zbl 1160.37439

Summary: In this letter, the global exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with time delays and Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the neural network is stochastically exponentially stable in the mean square, independent of the time delay. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions, and therefore the global exponential stability in the mean square for the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.

MSC:

37N99 Applications of dynamical systems
92B20 Neural networks for/in biological studies, artificial life and related topics
68T05 Learning and adaptive systems in artificial intelligence

Software:

LMI toolbox; Matlab
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Cao, J.; Ho, D. W.C., Chaos Solitons Fractals, 24, 5, 1317 (2005)
[2] Huang, H.; Cao, J., Appl. Math. Comput., 142, 1, 143 (2003)
[3] Liang, J.; Cao, J., Phys. Lett. A, 318, 1-2, 53 (2003)
[4] Wang, Z.; Liu, Y.; Liu, X., Phys. Lett. A, 345, 4-6, 299 (2005)
[6] Bolle, D.; Dupont, P.; Vinck, B., J. Phys. A, 25, 2859 (1992) · Zbl 0800.82013
[7] Casey, M. P., Neural Comput., 8, 6, 1135 (1996)
[8] Cleeremans, A.; Servan-Schreiber, D.; McClelland, J. L., Neural Comput., 1, 3, 372 (1989)
[9] Elman, J. L., Cognitive Sci., 14, 179 (1990)
[10] Tino, P.; Cernansky, M.; Benuskova, L., IEEE Trans. Neural Networks, 15, 1, 6 (2004)
[11] Kovacic, M., Eur. J. Oper. Res., 69, 1, 92 (1993)
[12] Ji, Y.; Chizeck, H. J., IEEE Trans. Automat. Control, 35, 777 (1990)
[13] Wang, Z.; Lam, J.; Liu, X., IEEE Trans. Signal Process., 51, 9, 2321 (2003)
[14] Boyd, S.; EI Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia
[15] Skorohod, A. V., Asymptotic Methods in the Theory of Stochastic Differential Equations (1989), American Mathematical Society: American Mathematical Society Providence, RI
[16] Gahinet, P.; Nemirovsky, A.; Laub, A. J.; Chilali, M., LMI Control Toolbox: For Use with Matlab (1995), The Math Works Inc.
[17] Gao, H.; Wang, C., IEEE Trans. Automat. Control, 48, 9, 1661 (2003)
[18] Gao, H.; Wang, C., IEEE Trans. Signal Process., 52, 6, 1631 (2004)
[19] Gao, H.; Lam, J.; Xie, L.; Wang, C., IEEE Trans. Signal Process., 53, 8, 3183 (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.