×

zbMATH — the first resource for mathematics

New and improved results on stability of static neural networks with interval time-varying delays. (English) Zbl 1334.93135
Summary: The problem of stability analysis for static neural networks with interval time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, new and improved delay-dependent stability criteria to guarantee the asymptotic stability of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by standard numerical packages. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum delay bounds.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
92B20 Neural networks for/in biological studies, artificial life and related topics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Gupta, M. M.; Jin, L.; Homma, N., Static and dynamic neural networks: from fundamentals to advanced theory, (2003), Wiley New York
[2] Xu, Z.; Qiao, H.; Peng, J.; Zhang, B., A comparative study of two modeling approaches in neural networks, Neural Networks, 17, 73-85, (2003) · Zbl 1082.68099
[3] Qiao, H.; Peng, J.; Xu, Z.; Zhang, B., A reference model approach to stability analysis of neural networks, IEEE Trans. Syst. Man Cybern. Part B: Cybern., 33, 925-936, (2003)
[4] Niculescu, S. I., Delay effects on stability: A robust control approach, (2001), Springer Berlin
[5] Richard, J. P., Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 1667-1694, (2003) · Zbl 1145.93302
[6] Xu, S.; Lam, J., A survey of linear matrix inequality techniques in stability analysis of delay systems, Int. J. Syst. Sci., 39, 1095-1113, (2008) · Zbl 1156.93382
[7] Park, Ju H.; Kwon, O. M.; Lee, S. M., LMI optimization approach on stability for delayed neural networks of neutral-type, Appl. Math. Comput., 196, 1, 236-244, (2008) · Zbl 1157.34056
[8] Park, Ju H.; Kwon, O. M., On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays, Appl. Math. Comput., 199, 2, 435-446, (2008) · Zbl 1149.34049
[9] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems, (2003), Birkhäuser · Zbl 1039.34067
[10] Ariba, Y.; Gouaisbaut, F., An augmented model for robust stability analysis of time-varying delay systems, Int. J. Control, 82, 1616-1626, (2009) · Zbl 1190.93076
[11] Xu, S.; Lam, J., A survey of linear matrix inequality techniques in stability analysis of delay systems, Int. J. Syst. Sci., 39, 1095-1113, (2008) · Zbl 1156.93382
[12] Seuret, A.; Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems, Automatica, 49, 2860-2866, (2013) · Zbl 1364.93740
[13] Park, P. G.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 235-238, (2011) · Zbl 1209.93076
[14] Kim, S. H.; Park, P.; Jeong, C. K., Robust \(\mathcal{H}_\infty\) stabilisation of networks control systems with packet analyser, IET Control Theory Appl., 4, 1828-1837, (2010)
[15] Kwon, O. M.; Park, M. J.; Lee, S. M.; Park, Ju H.; Cha, E. J., Stability for neural networks with time-varying delays via some new approaches, IEEE Trans. Neural Networks Learn. Syst., 24, 181-193, (2013)
[16] Shao, H., Delay-dependent stability for recurrent neural networks with time-varying delays, IEEE Trans. Neural Networks, 19, 1647-1651, (2008)
[17] Shao, H., Novel delay-dependent stability results for neural networks with time-varying delays, Circuits Syst. Signal Process., 29, 637-647, (2010) · Zbl 1196.93063
[18] Zuo, Z.; Yang, C.; Wang, Y., A new method for stability analysis of recurrent neural networks with interval time-varying delay, IEEE Trans. Neural Networks, 21, 339-344, (2010)
[19] Wu, Z.-G.; Lam, J.; Su, H.; Chu, J., Stability and dissipativity analysis of static neural networks with time delay, IEEE Trans. Neural Networks, 23, 199-210, (2012)
[20] Sun, J.; Chen, J., Stability analysis of static recurrent neural networks with interval time-varying delay, Appl. Math. Comput., 221, 111-120, (2013) · Zbl 1329.93119
[21] Li, X.; Gao, H.; Yu, X., A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays, IEEE Trans. Syst. Man Cybern.-Part B: Cybern., 41, 1275-1286, (2011)
[22] Bai, Y.-Q.; Chen, J., New stability criteria for recurrent neural networks with interval time-varying delay, Neurocomputing, 121, 179-184, (2013)
[23] Kharitonov, V. L.; Niculescu, S. I., On the stability of linear systems with uncertain delay, IEEE Trans. Autom. Control, 48, 127-132, (2013) · Zbl 1364.34102
[24] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004
[25] Li, T.; Zheng, W. X.; Lin, C., Delay-slope-dependent stability results of recurrent neural networks, IEEE Trans. Neural Networks, 22, 2138-2143, (2011)
[26] de Oliveira, M. C.; Skelton, R. E., Stability tests for constrained linear systems, (2001), Springer-Verlag Berlin, pp. 241-257 · Zbl 0997.93086
[27] Gu, K., A further refinement of discretized Lyapunov functional method for the stability of time-delay systems, Int. J. Control, 74, 967-976, (2001) · Zbl 1015.93053
[28] Kwon, O. M.; Park, Ju H.; Lee, S. M.; Cha, E. J., Analysis on delay-dependent stability for neural networks with time-varying delays, Neurocomputing, 103, 114-120, (2013)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.