Robust stabilization of stochastic Markovian jumping dynamical networks with mixed delays

Neurocomputing

Volumn 86, Issue , 2012, Pages 107-115

  Yu, Jinyong ^a   Sun, Guanghui ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Adaptive control; Markovian jumping; Mixed time delays; Stochastic systems

Indexed keywords

ADAPTIVE CONTROL; ADAPTIVE FEEDBACK; DISTRIBUTED DELAYS; DYNAMICAL NETWORKS; GLOBAL ASYMPTOTICAL STABILITY; MARKOVIAN; MARKOVIAN JUMPING PARAMETERS; MEAN SQUARE; MIXED DELAYS; ROBUST ADAPTIVE STABILIZATION; ROBUST STABILIZATION; THEORETICAL RESULT; TIME-VARYING DELAY;

UNCERTAINTY ANALYSIS;

STOCHASTIC SYSTEMS;

ARTICLE; MACHINE LEARNING; PRIORITY JOURNAL; STOCHASTIC MARKOVIAN JUMPING DYNAMICAL NETWORK; THEORETICAL MODEL;

EID: 84862778912     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2012.01.021     Document Type: Article

References (47)

1. Arenas A., Díaz-Guilera A., Pérez-Vicente C.J. Synchronization processes in complex networks. Phys. D: Nonlinear Phenom. 2006, 22:427-434.
2. Liu Y., Wang Z., Liu X. Exponential synchronization of complex networks with Markovian jump and mixed delays. Phys. Lett. A 2008, 372(22):3986-3998.
3. Lü J., Chen G. A time-varying complex dynamical network models and its controlled synchronization criteria. IEEE Trans. Autom. Control 2005, 50:841.
4. Tang Y., Wang Z., Fang J. Pinning control of fractional-order weighted complex networks. Chaos 2009, 19:013112.
5. Arik S. Stability analysis of delayed neural networks. IEEE Trans. Circuits Syst. I 2000, 47:1089-1092.
6. Singh V. Global robust stability of delayed neural networks: an LMI approach. IEEE Trans. Circuits Syst. II 2005, 52:33-36.
7. Chen T., Rong L. Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Trans. Neural Networks 2006, 15:203-206.
8. Huang H., Qu Y., Li H.X. Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Phys. Lett. A 2005, 345(4-6):345-354.
9. Liao X., Wong K., Wu Z., Chen G. Novel robust stability criteria for interval-delayed Hopfield neural networks. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 2001, 48(11):1355-1359.
10. Kwon O.M., Park J.H. On improved delay-dependent robust control for uncertain time-delay systems. IEEE Trans. Autom. Control 2004, 49(11):1991-1995.
11. Xu S., Lam J., Ho D.W.C. Novel global robust stability criteria for interval neural networks with multiple time-varying delays. Phys. Lett. A 2005, 342:322-330.
12. Wan L., Sun J. Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A 2005, 343:306-318.
13. Shi P., Zhang J., Qiu J., Xing L. New global asymptotic stability criterion for neural networks with discrete and distributed delays. Proc. IMechE J. Syst. Control Eng. 2006, 221(I1):129-135.
14. Cao J., Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I, Reg. Papers 2005, 52:417-426.
15. Cao J., Huang D.-S., Qu Y. Global robust stability of delayed recurrent neural networks. Chaos Solitons Fractals 2005, 23(1):221-229.
16. Cao J., Song Q. Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 2006, 19(7):1601-1617.
17. Tang Y., Fang J., Miao Q. Synchronization of stochastic delayed neural networks with Markovian switching and its application. Int. J. Neural Syst. 2009, 19:43-56.
18. Tang Y., Fang J. Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling. Neurocomputing 2009, 72:3253-3262.
19. Tang Y., Fang J., Xia M., Gu X. Synchronization of Takagi-Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays. Appl. Math. Modelling 2010, 34:843-855.
20. Wang Z., Fang J.a., Liu X. Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fractals 2008, 36:388-396.
21. Wang Z., Liu Y., Yu L., Liu X. Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 2006, 356(4-5):346-352.
22. Liu Y., Wang Z., Liu X. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks 2006, 19(5):667-675.
23. Liu Y., Wang Z., Liu X. On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching. Nonlinear Dynamics 2008, 54:199-212.
24. Dong H., Wang Z., Ho D.W.C., Gao H. Robust H-infinity filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: the finite-horizon case. IEEE Trans. Signal Process. 2011, 59:3048-3057.
25. Tino P., Cernansky M., Benuskova L. Markovian architectural bias of recurrent neural networks. IEEE Trans. Neural Networks 2004, 15(1):6-15.
26. Ge S.S., Hong F., Lee T. Robust adaptive control of nonlinear systems with unknown time delays. Automatica 2005, 41:1181-1190.
27. Ge S.S., Hong F., Lee T. Adaptive neural network control of nonlinear systems with unknown time delays. IEEE Trans. Autom. Control 2003, 48(12):2004-2010.
28. Huang D.B. Simple adaptive-feedback controller for identical chaos synchronization. Phys. Rev. E 2005, 71:037203.
29. Huang D.B. Adaptive-feedback control algorithm. Phys. Rev. E 2006, 73:066204.
30. Lu J., Cao J. Synchronization-based approach for parameters identification in delayed chaotic neural networks. Physica A 2007, 384:432-443.
31. Sun Y., Cao J. Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation. Phys. Lett. A 2007, 364:277-285.
32. Yu W., Cao J., Chen G. Robust adaptive control of unknown modified Cohen-Grossberg neural networks with delays. IEEE Trans. Circuits Syst. II 2007, 54(6).
33. Tang Y., Wang Z., Wong W.K., Kurths J., Fang J. Multiobjective synchronization of coupled systems. Chaos 2011, 21:025114.
34. Cao J., Wang Z., Sun Y. Synchronization in an array of linearly stochastically coupled networks with time delays. Physica A 2007, 385:718-728.
35. Tang Y., Qiu R., Fang J.A., Miao Q., Xia M. Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 2008, 372:4425-4433.
36. Tang Y., Wang Z., Fang J. Controller design for synchronization of an array of delayed neural networks using a controllable probabilistic PSO. Inf. Sci. 2011, 181:4715-4732.
37. ∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans. Autom. Control 2003, 48:900-907.
38. Khasminskii R. Stochastic Stability of Differential Equations 1980, Sijthoffand Noor, Khasminskiidhoff, Alphen aan den Rijn.
39. Skorohod A.V. Asymptotic Methods in the Theory of Stochastic Differential Equations 1989, Amer. Math. Soc., Providence.
40. Mao X. A note on the LaSalle-type theorems for stochastic differential delay equations. J. Math. Anal. Appl. 2002, 268:125-142.
41. Tang Y., Fang J., Xia M., Yu D. Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed time-varying delays. Neurocomputing 2009, 72:3830-3838.
42. Shen B., Wang Z., Liu X. Bounded H-infinity synchronization and state estimation for discrete time-varying stochastic complex networks over a finite-horizon. IEEE Trans. Neural Networks 2011, 22:145-157.
43. W. Zhang, Y. Tang, J. Fang, W. Zhu, Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances, Chaos 21 (2011) 043137, doi:. http://dx.doi.org/10.1063/1.3671609.
44. Shen B., Wang Z., Liu X. A stochastic sampled-data approach to distributed H-infinity filtering in sensor networks. IEEE Trans. Circuits Syst.-Part I 2011, 58:2237-2246.
45. Tang Y., Wang Z., Fang J. Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm. Expert Syst. Appl. 2011, 38:2523-2535.
46. Dong H., Wang Z., Ho D.W.C., Gao H. Robust H-infinity fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements. IEEE Trans. Fuzzy Syst. 2010, 18:712-725.
47. Tang Y., Wang Z., Fang J. Feedback learning particle swarm optimization. Appl. Soft Comput. 2011, 11:4713-4725.