Novel stability criteria for neutral systems with multiple time delays

Abstract Based on the eigenvalues of characteristic equations, some new criteria are derived to ensure the asymptotic stability for a class of neutral differential equations with multiple time delays. Conditions obtained here are independent of the time delays and easy to be checked. When suitable f j (·) ( j  = 1, 2, … ,  m ) are chosen, the model studied in this paper will reduce to a simple form. Moreover, our results can resolve some nonlinear neutral problems which are seldom discussed. Finally, an example with numerical simulation is given to show the effectiveness of our method.

[1]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[2]  A. Bellen,et al.  Methods for linear systems of circuit delay differential equations of neutral type , 1999 .

[3]  Cao Jinde.  Periodic solutions of a class of higher order neutral type equations , 1999 .

[4]  J. H. Park,et al.  Asymptotic Stability of Neutral Systems with Multiple Delays , 1999 .

[5]  C. Lien,et al.  Stability Conditions for a Class of Neutral Systems with Multiple Time Delays , 2000 .

[6]  Wei Zhang,et al.  Delay-dependent asymptotic stability of a two-neuron system with different time delays , 2006 .

[7]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[8]  J. Chou,et al.  Criteria for asymptotic stability of a class of neutral systems via a LMI approach , 2001 .

[9]  Wanyi Chen.  Comment on 'Simple criteria for stability of neutral systems with multiple delays' , 1999, Int. J. Syst. Sci..

[10]  Jinde Cao,et al.  Further investigate on periodic solutions of pth order delayed NDEs , 2002, Appl. Math. Comput..

[11]  Qiang Zhang,et al.  Stability analysis for cellular neural networks with variable delays , 2006 .

[12]  Tianping Chen,et al.  Robust synchronization of delayed neural networks based on adaptive control and parameters identification , 2006 .

[13]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[14]  Chang-Hua Lien,et al.  New stability criterion for a class of uncertain nonlinear neutral time-delay systems , 2001, Int. J. Syst. Sci..

[15]  Jinde Cao,et al.  Discussion of periodic solutions for pth order delayed NDEs , 2002, Appl. Math. Comput..

[16]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[17]  Guang-Di Hu,et al.  Technical note Simple criteria for stability of neutral systems with multiple delays , 1997, Int. J. Syst. Sci..

[18]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[19]  Baruch Cahlon,et al.  Algebraic criteria for stability of linear neutral systems with a single delay , 2001 .

[20]  D. A. Suzuki,et al.  A constructive algorithm for stabilization of nonlinear neutral time-delayed systems occurring in bioengineering , 1996, Int. J. Syst. Sci..

[21]  Si Jianguo.  Discussion on the periodic solutions for higher-order linear equation of neutral type with constant coefficients , 1996 .

[22]  Erik I. Verriest,et al.  Stability and Control of Time-delay Systems , 1998 .

[23]  X. Lou,et al.  Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2006 .

[24]  Ping He,et al.  Algebraic stability criteria of linear neutral systems with multiple time delays , 2004, Appl. Math. Comput..

[25]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.