Robust stability of cellular neural networks with delay: Linear matrix inequality approach

IEE Proceedings: Control Theory and Applications

Volumn 151, Issue 1, 2004, Pages 125-129

  Singh, V ^a  

^a ATILIM UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; IMAGE PROCESSING; MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); VECTORS;

CELLULAR NEURAL NETWORKS (CNN); LINEAR MATRIX INEQUALITIES (LMI);

NEURAL NETWORKS;

EID: 1542790694     PISSN: 13502379     EISSN: None     Source Type: Journal    
DOI: 10.1049/ip-cta:20040091     Document Type: Conference Paper

References (50)

1. Chua, L.O., and Yang, L.: 'Cellular neural networks: Theory', IEEE Trans. Circuits Syst., 1988, 35, (10), pp. 1257-1272
2. Roska, T., Boros, T., Thiran, P., and Chua, L.O.: 'Detecting simple motion using cellular neural networks'. Proc. IEEE Int. Workshop on Cellular Neural Networks and their Applications, 1990, pp. 127-138
3. Chua, L.O., and Roska, T.: 'Cellular neural networks with nonlinear and delay-type template elements'. Proc. IEEE Int. Workshop on Cellular Neural Networks and their Applications, 1990, pp. 12-25
4. Kim, H., Roska, T., Son, H., and Petras, I.: 'Analog addition/substraction on the CNN-UM chip with short-time superimposition of input signals', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2003, 50, (3), pp. 429-432
5. Roska, T., Wu, C.W., Balsi, M., and Chua, L.O.: 'Stability and dynamics of delay-type general and cellular neural networks', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 1992, 39, (6), pp. 487-490
6. Roska, T., Wu, C.W., and Chua, L.O.: 'Stability of cellular neural networks with dominant nonlinear and delay-type templates', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 1993, 40, (4), pp. 270-272
7. Civalleri, P.P., Gilli, M., and Pandolfi, L.: 'On stability of cellular neural networks with delay', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 1993, 40, (3), pp. 157-164
8. Su, J., Hu, A.Q., and He, Z.Y.: 'Stability analysis of analogue neural networks', Electron. Lett., 1997, 33, (6), pp. 506-507
9. Civalleri, P.P., and Gilli, M.: 'Practical stability criteria for cellular neural networks', Electron. Lett., 1997, 33, (11), pp. 970-971
10. Arik, S., and Tavsanoglu, V.: 'Equilibrium analysis of delayed CNNs', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 1998, 45, (2), pp. 168-171
11. Perfetti, R.: 'Some stability criteria for cellular neural networks with sigmoidal nonlinearities', Electron. Lett., 1999, 35, (3), pp. 227-228
12. Gilli, M.: 'Design of stable cellular neural network templates'. Electron. Lett., 1999, 35, (12), pp. 986-987
13. Liao T.L. WangF.C.: 'Global stability condition for cellular neural networks with delay' Electron. Lett. 1999 35 (16) pp. 1347-1349
14. Arik, S., and Tavsanoglu, V.: 'On the global asymptotic stability of delayed cellular neural networks', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2000, 47, (4), pp. 571-574
15. Liao, T.L., and Wang, F.C.: 'Global stability for cellular neural networks with time delay', IEEE Trans. Neural Netw., 2000, 11, (6), pp. 1481-1484
16. Takahashi, N.N.: 'A new sufficient condition for complete stability of cellular neural networks with delay', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2000, 47, (6), pp. 793-799
17. Zhang, Q., Ma, R.N., and Xu, J.: 'Stability of cellular neural networks with delay', Electron. Lett., 2001, 37, (9), pp. 575-576
18. Cao, J.: 'A set of stability criteria for delayed cellular neural networks', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2001, 48, (4), pp. 494-498
19. Yi, Z., Heng, P.A., and Leung, K.S.: 'Convergence analysis of cellular neural networks with unbounded delay', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2001, 48, (6), pp. 680-687
20. Cao, J.: 'Global stability conditions for delayed CNNs', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2001, 48, (11), pp. 1330-1333
21. Arik, S.: 'An analysis of global asymptotic stability of delayed cellular neural networks', IEEE Trans. Neural Netw., 2002, 13, (5), pp. 1239-1242
22. Liao, X., Chen, G., and Sanchez, E.N.: 'LMI-based approach for asymptotically stability analysis of delayed neural networks', IEEE Trans. Circuits Syst. I. Fundam. Theory Appl., 2002, 49, (7), pp. 1033-1039
23. Arik, S.: 'An improved global stability result for delayed cellular neural networks', IEEE Trans. Circuits Syst. I., Fundam. Theory Appl., 2002, 49, (8), pp. 1211-1214
24. Cao, J., and Wang, J.: 'Global asymptotic stability of recurrent neural networks with Lipschitz-continuous activation functions and time-varying delays', IEEE Trans. Circuits Syst. I., Fundam. Theory Appl., 2003, 50, (1), pp. 34-44
25. Cao, J., and Zhou, D.: 'Stability analysis of delayed cellular neural networks', Neural Netw., 1998, 11, (9), pp. 1601-1605
26. Liao, X., and Yu, J.: 'Robust stability for interval Hopfield neural networks with time delay', IEEE Trans. Neural Netw., 1998, 9, (5), pp. 1042-1046
27. Liao, X., Wong, K., Wu, Z., and Chen, G.: 'Novel robust stability criteria for interval-delayed Hopfield neural networks', IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 2001, 48, (11), pp. 1355-1359
28. Arik, S.: 'Global robust stability of delayed neural networks', IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 2003, 50, (1), pp. 156-160
29. Cao, J.: 'Global stability analysis in delayed cellular neural networks', Phys. Rev. E, 1999, 59, (5), pp. 5940-5944
30. Arik, S.: 'Stability analysis of delayed neural networks', IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 2000, 47, (7), pp. 1089-1093
31. Zhang, J.Y., and Yang, Y.R.: 'Global stability analysis of bidirectional associative memory neural networks with delay', Int. J. Circuit Theory Appl., 2001, 29, (2), pp. 185-196
32. Liao, X.F., Wong, K.W., and Yu, J.: 'Novel stability conditions for cellular neural networks with time delay', Int. J. Bifurcation Chaos, 2001, 11, (7), pp. 1853-1864
33. Cao, J.D., and Wang, L.: 'Exponential stability and periodic oscillatory solution in BAM networks with delays', IEEE Trans. Neural Netw., 2002, 13, (2), pp. 457-463
34. Chen, T.: 'Global exponential stability of delayed Hopfield neural networks', Neural Netw., 2001, 14, (8), pp. 977-980
35. Liao, X., Chen, G., and Sanchez, E.: 'Delay-dependent exponential stability analysis of delayed neural networks', Neural Netw., 2002, 15, (7), pp. 855-866
36. Peng, J., Qiao, H., and Xu, Z.: 'A new approach to the stability of neural networks with time-varying delays', Neural Netw., 2002, 15, (1), pp. 95-103
37. Yi, Z., Heng, P.A., and Vadakkepat, P.: 'Absolute periodicity and absolute stability of delayed neural networks', IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 2002, 49, (2), pp. 256-261
38. Zhang, J.: 'Absolute exponential stability in delayed cellular neural networks', Int. J. Circuit Theory Appl., 2002, 30, (4), pp. 395-409
39. Hu, S.Q., and Wang, J.: 'Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks', IEEE Trans. Autom. Control, 2002, 47, (5), pp. 802-807
40. Qiang, Z., Ma, R.N., Chao, W., and Xu, J.: 'On the global stability of delayed neural networks', IEEE Trans. Autom. Control, 2003, 48, (5), pp. 794-797
41. Zhang, J.Y., and Jin, X.S.: 'Global stability analysis in delayed Hopfield neural network models', Neural Netw., 2000, 13, (7), pp. 745-753
42. Chen, Y.M.: 'Global stability of neural networks with distributed delays', Neural Netw., 2002, 15, (7), pp. 867-871
43. ∞ control theory', IEEE Trans. Autom. Control, 1990, 35, (3), pp. 356-361
44. ∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback', IEEE Trans. Autom. Control, 1992, 37, (8), pp. 1253-1256
45. Du, C., and Xie, L.: 'Stability analysis and stabilization of uncertainz two-dimensional discrete systems: an LMI approach', IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 1999, 46, (11), pp. 1371-1374
46. Guan, X., Long, C., and Duan, G.: 'Robust optimal guaranteed cost control for 2D discrete systems', IEE Proc., Control Theory Appl., 2001, 148, (5), pp. 355-361
47. ∞ filtering with regional pole assignment for uncertain discrete-time systems', IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 2002, 49, (8), pp. 1236-1241
48. Xu, S., Lam, J., Lin, Z., and Galkowski, K.: 'Positive real control for uncertain two-dimensional systems', IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 2002, 49, (11), pp. 1659-1666
49. Boyd, S., Ghaoui, L.E., Feron, E., and Balakrishnan, V.: 'Linear matrix inequalities in system and control theory' (SIAM, Philadelphia, PA, 1994)
50. Cabinet, P., Nemirovski, A., Laub, A.J., and Chilali, M.: 'LMI control toolbox for use with Matlab' (The MATH Works Inc., 1995)