Browse > Article
http://dx.doi.org/10.5370/KIEE.2011.60.2.376

Delay-dependent Stability Criteria for Fuzzy Markovian Jumping Hopfield Neural Networks of Neutral Type with Time-varying Delays  

Park, Myeong-Jin (충북대학교 전기공학부)
Kwon, Oh-Min (충북대학교 전기공학부)
Park, Ju-Hyun (영남대학교 전기공학과)
Lee, Sang-Moon (대구대학교 전자공학부)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.60, no.2, 2011 , pp. 376-382 More about this Journal
Abstract
This paper proposes delay-dependent stability conditions of the fuzzy Markovian jumping Hopfield neural networks of neutral type with time-varying delays. By constructing a suitable Lyapunov-Krasovskii's (L-K) functional and utilizing Finsler's lemma, new delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. A numerical example is given to illustrate the effectiveness of the proposed methods.
Keywords
Hopfield neural networks; Fuzzy systems; Neutral systems; Time-varying delays; Markovian jumping parameters; Lyapunov method; LMI;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 M.C. de Oliveira, R.E. Skelton. Stability tests for constrained linear systems. Springer, Berlin, 2001.
2 S. Boyd, L.EI Ghaoui and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, 1994.
3 M.S. Ali, P. Balasubramaniam, "Stability analysis of uncertain fuzzy Hofield neural networks with time delay", Commun. Nonlinear Sci. Numer. Simmul., vol.14, pp.2776-2783, 2009.   DOI   ScienceOn
4 P. Balasubramaniam, R. Rakkiyappan, R. Sathy, "Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters", Expert Syst. Appl., vol.38, pp.121-130, 2011.   DOI   ScienceOn
5 B. Liu, P. Shi, "Delay-range-dependent stability for fuzzy BAM neural networks with time-varying delays", Phys. Lett. A, vol.373, pp.1830-1838, 2009.   DOI   ScienceOn
6 Z. Fei, H. Gao, P. Shi, "New results on stabilization of Markovian jump systems with time delay", Automatica, vol.45, pp.2300-2306, 2009.   DOI   ScienceOn
7 E. Tian, D. Yue, Y. Zhang, "Delay-dependent robust $H{\infty}$ control for T-S fuzzy system with interval time-varying delay", Fuzzy Sets Syst., vol.160, pp.1708-1719, 2009.   DOI   ScienceOn
8 O.M. Kwon, Ju H. Park, S.M. Lee, "Delay-dependent Stability Criteria for Uncertain Stochastic Neural Networks with Interval Time-varying Delays", The Transactions of The Korean Institute of Elecetrical Engineers (KIEE), vol.57, pp.2066-2073, 2008.
9 T. Takagi, M. Sugeno, "Fuzzy Identification of Systems and Its Applications to Modeling and Control", IEEE Trans. Syst. Man Cybern., vol.15, pp.116-132, 1985.
10 X. Mao, "Exponential Stability of Stochastic Delay Interval Systems With Markovian Switching", IEEE Trans. Autom. Control, vol.47, pp.1604-1612, 2002.   DOI   ScienceOn
11 H. Liu, L. Zhao, Z. Zhang, Y. Ou, "Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays", Neurocomputing, vol.72, pp.3669-3674, 2009.   DOI   ScienceOn
12 D. Yang, C. Hu, "Novel delay-dependent global asymptotic stability condition of Hopfield neural networks with delays", Comput. Math. Appl., vol.57, pp.1978-1984, 2009.   DOI   ScienceOn
13 K. Gu, "An integral inequality in the stability problem of time-delay systems", in: The 39th IEEE Conf. Decision Control, Sydney, Australia, Dec. 2000, pp.2805-2810.
14 Ju H. Park, O.M. Kwon, "Global stability for neural networks of neutral-type with interval time-varying delays", Chaos Solitons Fractals, vol.41, pp.1174-1181, 2009.   DOI   ScienceOn
15 X.-D. Zhao, Q.-S. Zeng, "Delay-dependent stability analysis for Markovian jump systems with interval time-varying delays", Int. J. Autom. Comput., vol.7, pp.224-229, 2010.   DOI   ScienceOn
16 J.J. Hopfield, "Neural networks and physical systems with emergent collect computational abilities", Proc. Nat. Acad. Sci. USA, vol.79, pp.2554-2558, 1982.   DOI   ScienceOn
17 X. Lou, B. Cui, "New LMI conditions for delay-dependent asymptotic stability of delayed Hopfiled neural networks", Neurocomputing, vol.69, pp.2374-2378, 2006.   DOI   ScienceOn
18 S. Mou, H. Gao, J. Lam, W. Qiang, "A New Criterion of Delay-Dependent Asymptotic Stability for Hopfield Neural Networks With Time Delay", IEEE Trans. Neural Netw., vol.19, pp.532-535, 2008.   DOI   ScienceOn
19 B. Oksendal. Stochastic Differential Equations. Springer, Berlin, 2003.