Impulsive stabilization of delayed neural networks with and without uncertainty

International Journal of Robust and Nonlinear Control

Volumn 17, Issue 16, 2007, Pages 1489-1502

  Li, Chuandong ^a,b   Liao, Xiaofeng ^a  

^a HANGZHOU DIANZI UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Delayed neural networks; Impulsive stabilization; Linear matrix inequality (LMI); Uncertain systems

Indexed keywords

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; UNCERTAINTY ANALYSIS;

DIFFERENTIAL SYSTEMS; DYNAMICAL BEHAVIOURS; IMPULSIVE STABILIZATION;

HOPFIELD NEURAL NETWORKS;

EID: 35448981079     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1183     Document Type: Article

References (23)

1. Lakshmikantham V, Bainov DD, Simeonov PS. Theory of Impulsive Differential Equations. World Scientific: Singapore, 1989.
2. Samoilenko AM, Perestyuk NA. Impulsive Differential Equations. World Scientific: Singapore, 1995.
3. Anokhin AV. On linear impulsive systems for functional differential equations. Soviet Mathematical Doklady 1986; 33:220-223.
4. Yan JS, Shen JH. Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions. Nonlinear Analysis 1999; 37:245-255.
5. Lakshmikantham V, Liu X. Stability Analysis in Terms of Two Measures. World Scientific: Singapore, 1993.
6. Yang T. Impulsive Control Theory. Springer: Berlin, 2001.
7. Zhang B, Liu Y. Global attractivity for 'certain impulsive' delay differential equations. Nonlinear Analysis 2003; 52:725-736.
8. Tang S, Chen L. Global attractivity in a "food-limited" population model with impulsive effects. Journal of Mathematical Analysis and Applications 2004; 292:211-221.
9. Liu X. Impulsive stabilization and control of chaotic system. Nonlinear Analysis 2001; 47:1081-1092.
10. Li CD, Liao XF. Complete and lag synchronization of chaotic systems via small pulses. Chaos, Solitons & Fractals 2004; 22:857-867.
11. Li CD, Liao XF, Zhang XY. Impulsive synchronization of chaotic systems. Chaos 2005; 15:023104.
12. Guan ZH, Chen GR. On delayed impulsive Hopfield neural networks. Neural Networks 1999; 12:273-280.
13. Li YK, Lu L. Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses. Physics Letters A 2004; 333:62-71.
14. Akca H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E. Continuous-time additive Hopfield-type neural networks with impulses. Journal of Mathematical Analysis and Applications 2004; 290:436-451.
15. Li CD, Liao XF. Delay-dependent exponential stability analysis of bi-directional associative memory neural networks: an LMI approach. Chaos, Solitons & Fractals 2005; 24:1119-1134.
16. Liao XF, Li CD. An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D 2005; 200:139-155.
17. Li CD, Liao XF, Zhang R. Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach. Physics Letters A 2004; 328:452-462.
18. Li CD, Liao XF. New algebraic conditions for global exponential stability of delayed recurrent neural networks. Neurocomputing 2005; 64C:319-333.
19. Zhang Y, Pheng Ann Heng, Vadakkepat P. Absolute periodicity and absolute stability of delayed neural networks. IEEE Transactions on Circuits and Systems - I 2002; 49:256-261.
20. Sanchez EN, Perez JP. Input-to-state stability analysis for dynamic NN. IEEE Transactions on Circuits Systems 1999; 46:1395-1398.
21. Boyd S, Ghaoui L El, Feron, E, Balakrishnan V. Linear Matrix Inequalities in Systems and Control Theory. SIAM: Philadelphia, PA, 1994.
22. Liu B, Liu X, Liao XX. Robust stability of uncertain impulsive dynamical systems. Journal of Mathematical Analysis and Applications 2004; 290:519-533.
23. Lu HT. Chaotic attractors in delayed neural networks. Physics Letters A 2002; 298:109-116.