A New Stability Criterion of a Class of Neutral Differential Equations

뉴트럴 미분방정식의 새로운 안정성 판별법

  • 권오민 (충북대학교 전기공학과) ;
  • 박주현 (영남대학교 전기공학과)
  • Published : 2007.11.01

Abstract

In this letter, the problem for a class of neutral differential equation is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both ${\tau}\;and\;{\sigma}$, is derived in terms of linear matrix inequality (LMI). Two numerical examples are carried out to support the effectiveness of the proposed method.

Keywords

References

  1. J. Hale, and S.M.V. Lunel, Introduction to Functional Differential Equatins, Springer- Verlag, New York, 1993
  2. V.B. Kolmanovskii,. and A. Myshkis, Applied Theory to Functional Differential Equations, Kluwer Academic Publishers, Boston, 1992
  3. G.D. Hu, and G.D. Hu, 'Some Simple Stability Criteria of Neutral-Differential Systems', Applied Mathematics and Computation, vol. 80, pp.257-271, 1996 https://doi.org/10.1016/0096-3003(95)00301-0
  4. O.M. Kwon, and J.H. Park, 'An Improved Delay-Dependent Robust Control for Uncertain TIme-Delay Systems', IEEE Trans. on Automatic Control, vol. 49, No. 11, pp.1991-1995, 2004 https://doi.org/10.1109/TAC.2004.837563
  5. J.H. Park, S. Won, 'Asymptotic Stability of Neutral Systems with Multiple Delays', Journal of Optimization Theory and Applications, vol. 103, pp.187-200, 1999
  6. K. Gopalsamy, I. Leung, and P. Liu, 'Global Hopf'-bifuration in a Neural Netlet', Applied Mathematics and Computation, vol. 94, pp.171-192, 1998 https://doi.org/10.1016/S0096-3003(97)10087-X
  7. H.A. El-Morshedy and K. Gopalsamy, 'Nonoscillation, Oscillation and Convergence of a Class of Neutral Equations', Nonlinear Analysis, vol. 40, pp.173-183, 2000 https://doi.org/10.1016/S0362-546X(00)85010-5
  8. R.P. Agarwal and S.H. Grace, 'Asymptotic Stability of Certain Neutral Differential Equations', Mathematical and Computer Modelling, vol.31, pp.9-15, 2000
  9. J.H. Park, 'Delay-Dependent Criterion for Asymptotic Stability of a Class of Neutral Equations', Applied Mathematics Letters, vol. 17, pp.1203-1206, 2004 https://doi.org/10.1016/j.aml.2003.05.013
  10. J.H. Park, and O.M. Kwon, 'Stability Analysis of Certain Nonlinear Differential Equation', Chaos Solitons & Fractals, doi:10.1016/j.chaos.2006.09.015
  11. C. Li, X. Liao, and R. Zhang, 'Delay-Dependent Exponential Stability Analysis of Bi-Directional Associative Memory Neural Networks with Time Delay', Chaos Solitons & Fractals, vol. 24, pp.1119-1134, 2005 https://doi.org/10.1016/j.chaos.2004.09.052
  12. J.H. Park, 'Global Exponential Stability of Cellular Neural Networks with Variable Delays', Applied Mathematics and Computation, vol. 183, 1214-1219, 2006 https://doi.org/10.1016/j.amc.2006.06.046
  13. S. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Philadelphia, SIAM, 1994
  14. P. Gahinet, A. Nemirovski, A. Laub, M. GChilali, LMI Control Toolbox User's Guide, The Mathworks, Natick, Massachusetts, 1995