Global Uniform Asymptotic Stability of Memristor-Based Recurrent Neural Networks With Time Delays

HU Jin; SONG Qian-kun

doi:10.3879/j.issn.1000-0887.2013.07.007

Volume 34 Issue 7

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2013 > 34(7): 724-735

HU Jin, SONG Qian-kun. Global Uniform Asymptotic Stability of Memristor-Based Recurrent Neural Networks With Time Delays[J]. Applied Mathematics and Mechanics, 2013, 34(7): 724-735. doi: 10.3879/j.issn.1000-0887.2013.07.007

Citation:

PDF( 672 KB)

Global Uniform Asymptotic Stability of Memristor-Based Recurrent Neural Networks With Time Delays

doi: 10.3879/j.issn.1000-0887.2013.07.007

Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

Received Date: 2013-05-07
Rev Recd Date: 2013-05-09
Publish Date: 2013-07-15

Abstract

Abstract

Memristor is a newly prototyped nonlinear circuit device. Its value is not unique and changes according to the value of the magnitude and polarity of the voltage applied to it. Due to this feature, the memristor has the function of memory and broad potential applications of memristors have been reported in various fields. A simplified mathematical model was proposed to characterize the pinched hysteresis feature of the memristor and a memristor-based recurrent neural network model was given. With the theory of differential inclusion, Lyapunov approach and homeomorphism theory, the existence and uniqueness of the equilibrium point of the model were obtained, and the global uniform asymptotic stability of memristor-based recurrent neural networks was also obtained. Finally, the simulation result shows the efficiency of the theorem.
- memristor,
- recurrent neural network,
- global uniform asymptotic stability,

FullText(HTML)

References(24)

References

[1]	Strukov D B, Snider G S, Stewart D R, Williams R S. The missing memristor found[J].Nature,2008, 453(7191): 80-83.
[2]	Chua L O. Memristor the missing circuit element[J].IEEE Transactions on Circuit Theory,1971, 18(5): 507-519.
[3]	Pershin Y V, Ventra M D. Spin memristive systems: spin memory effects in semiconductor spintronics[J].Physical Review B,2008, 78(11): 1-4.
[4]	Yang J J, Pickett M D, Li X, Ohlberg D A A, Stewart D R, Williams R S.Memristive switching mechanism for metal/oxide/metal nanodevices[J].Nature Nanotechnology,2008, 3(7): 429-433.
[5]	Wang X, Chen Y, Xi H, Li H, Dimitrov D. Spintronic memristor through-spin-torqueinduced magnetization motion[J].IEEE Electron Device Letters,2009, 30(3): 294-297.
[6]	Xia Y, Wang J. Global asymptotic and exponential stability of a dynamic-neural system with asymmetric connection weights[J].IEEE Transactions on Automatic Control,2001, 46(4): 635-638.
[7]	Hu S, Wang J. Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks[J].IEEE Transactions on Automatic Control,2002, 46(5):802-807.
[8]	Cao J, Wang J. Global asymptotic stability of a general class of recurrent neural network with time-varing delays[J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2003, 50(1): 34-44.
[9]	Zhang J. Globally exponential stability of neural networks with variable delays[J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2003, 50(2): 288-291.
[10]	Zeng Z, Wang J, Liao X. Global exponential stability of a general class of recurrent neural networks with timevarying delays[J].IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003, 50(10): 1353-1358.
[11]	Cao J, Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays[J].IEEE Transactions on Circuits and Systems I: Regular Papers,2005, 52(2): 417-426.
[12]	Liao X, Wang J, Zeng Z. Global asymptotic stability and global exponential stability of delayed cellular neural networks[J].IEEE Transactions on Circuits and Systems II: Express Briefs,2005, 52(7): 168-173.
[13]	Zeng Z, Wang J, Liao X. Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays[J].IEEE Transactions on Circuits and Systems II: Express Briefs,2005, 52(3): 403-409.
[14]	Cao J, Yuan K, Li H. Global asymptotical stability of recurrent neural-networks with multiple discrete delays and distributed delays[J].IEEE Transactions on Neural Networks,2006, 17(6): 1646-1651.
[15]	Zeng Z, Wang J. Improved conditions for global exponential stability of recurrent neural networks with timevarying delays[J].IEEE Transactions on Neural Networks,2006, 17(3): 623-635.
[16]	Chen W, Zheng W. Global asymptotic stability of a class of neural networks with distributed delays[J].IEEE Transactions on Circuits and Systems I: Regular Papers,2006, 53(3): 244-252.
[17]	Yu W, Cao J, Wang J. An LMI approach to delayed global asymptotic stability of the Cohen-Grossberg neural networks via nonsmooth analysis[J]. Neural Networks,2007, 20(7): 810-818.
[18]	Chen W, Zheng W. On global asymptotic stability of Cohen-Grossberg neural networks with variable delays[J].IEEE Transactions on Circuits and Systems I: Regular Papers,2008, 55(10): 3145-3159.
[19]	Shen Y, Wang J. An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays[J].IEEE Transactions on Neural Networks,2008, 19(3): 528-531.
[20]	Filippov A F.Differential Equations With Discontinuous Right-Hand-Sides [M]. Dordrecht: Kluwer, 1988.
[21]	Paden B E, Sastry S S. A calculus for computing Filippov’s differential inclusions with applications to the variable structure control of robot manipulators[J].IEEE Transactions on Circuits and Systems,1987, 34(1): 73-82.
[22]	Bacciotti A, Rosier L.Liapunov Functions and Stability in Control Theory [M]. 2nd ed. Communications and Control Engineering. Vol 14. London: Springer, 2005.
[23]	Forti M, Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems[J].IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications,1995, 42(7): 354-366.
[24]	Berman A, Plemmons R J.Nonnegative Matrices in the Mathematical Sciences [M].New York: Academic Press, 1979.