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Global exponential stability for discrete-time neural networks with variable delays. (English) Zbl 1142.93393

Summary: This Letter provides new exponential stability criteria for discrete-time neural networks with variable delays. The main technique is to reduce exponential convergence estimation of the neural network solution to that of one component of the corresponding solution by constructing Lyapunov function based on M-matrix. By introducing the tuning parameter diagonal matrix, the delay-independent and delay-dependent exponential stability conditions have been unified in the same mathematical formula. The effectiveness of the new results are illustrated by three examples.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
37N35 Dynamical systems in control
34D05 Asymptotic properties of solutions to ordinary differential equations
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[1] Hopfield, J.J., Proc. natl. acad. sci. USA, 81, 3088, (1984)
[2] Cao, J., Phys. lett. A, 270, 157, (2000)
[3] Cao, J., Phys. lett. A, 267, 312, (2000)
[4] Xu, D.; Zhao, H.; Zhu, H., Comput. math. appl., 42, 39, (2001)
[5] Ye, H.; Michel, A.N., IEEE trans. circuits systems I, 43, 532, (1996)
[6] Zhang, J., IEEE trans. circuits systems I, 50, 288, (2003)
[7] Chen, W.-H.; Guan, Z.-H.; Lu, X., Phys. lett. A, 326, 355, (2004)
[8] Chen, W.-H.; Lu, X., Phys. lett. A, 351, 53, (2006)
[9] Cao, J., Phys. lett. A, 307, 136, (2003)
[10] Cao, J.; Wang, J., IEEE trans. circuits systems I, 52, 417, (2005)
[11] Cao, J.; Wang, J., IEEE trans. circuits systems I, 52, 920, (2005)
[12] Cao, J.; Wang, J., Neural networks, 17, 379, (2004)
[13] Marcus, C.M.; Westervelt, R.M., Phys. rev. A, 39, 347, (1989)
[14] Mohamad, S.; Gopalsamy, K., Appl. math. comput., 135, 17, (2003)
[15] Wang, L.; Zhou, X., Fields inst. commun., 43, 333, (2004)
[16] Xiong, W.; Cao, J., Neurocomputing, 64, 433, (2005)
[17] Li, Y., Phys. lett. A, 333, 51, (2004)
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.