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The local adaptive H∞ consistency is intensively investigated for delayed complex dynamical networks with noise. The network under consideration contains unknown but bounded nonlinear coupling functions and time-varying delays which appear in the coupling term and the node system simultaneously. Based on the Lyapunov stability theory, linear matrix inequality optimization technique and adaptive control, several local adaptive H∞ consistency schemes are established which guarantee robust asymptotically consistency for each node of noise-perturbed network as well as achieving a prescribed robust H∞ performance level. Finally, detailed and satisfactory numerical simulations validate the feasibility and the correctness of the proposed techniques.
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Keywords:
- H∞ consistency /
- delayed complex networks /
- noise /
- linear matrix inequality
[1] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[2] Wang X F, Chen G 2002 IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49 54
[3] Wang X F, Li X, Chen G R 2006 Theory and Application of Complex Networks (Beijing: Tsinghua University Press) p7 (in Chinese) [汪小帆, 李翔, 陈关荣 2006 复杂网络理论及其应用 (北京: 清华大学出版社) 第7页]
[4] Doyle J C, Alderson D L, Li L 2005 PNAS 102 14497
[5] Wang X F, Chen G R 2002 Physica A 310 521
[6] Kocarev L, Amato P 2005 Chaos 15 024101
[7] Zhou J, Chen T 2006 IEEE Trans. Circuits Syst. I 53 733
[8] Tu L L, Lu J A 2009 Comput. Math. Appl. 57 28
[9] Zhang Q J, Lu J A, L J H 2008 IEEE Trans. Circuits Syst. II 55 183
[10] Liu J L 2013 Acta Phys. Sin. 62 040503 (in Chinese) [刘金良 2013 物理学报 62 040503]
[11] Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 物理学报 62 018901]
[12] Aldana M, Ballezaa E, Kauffmanb S, Resendiz O 2007 J. Theor. Biol. 245 433
[13] Liang J L, Wang Z D, Liu X H 2008 Nonlinear Dyn. 53 153
[14] Park J H, Lee S M, Jung H Y 2009 J. Optim. Theory Appl. 143 357
[15] Li H J, Yue D 2010 J. Phys. A: Math. Theor. 43 105101
[16] Li Z K, Duan Z S, Chen G R 2009 Chin. Phys. B 18 5228
[17] Ke C, Wang Z M, Tu L L 2013 Acta Phys. Sin. 62 010508 (in Chinese) [柯超, 王志明, 涂俐兰 2013 物理学报 62 010508]
[18] Wei R, Wang X Y 2004 Acta Phys. Sin. 53 3298 (in Chinese) [魏荣, 王行愚 2004 物理学报 53 3298]
[19] Wang Z Y, Huang L H, Zuo Y, Zhang L L 2010 Int. J. Control Automat. Syst. 8 266
[20] Lin T C, Kuo C H 2011 ISA Trans. 50 548
[21] Ahn C K, Jung S T, Kang S K, Joo S C 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 2168
[22] Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM)
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[1] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[2] Wang X F, Chen G 2002 IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49 54
[3] Wang X F, Li X, Chen G R 2006 Theory and Application of Complex Networks (Beijing: Tsinghua University Press) p7 (in Chinese) [汪小帆, 李翔, 陈关荣 2006 复杂网络理论及其应用 (北京: 清华大学出版社) 第7页]
[4] Doyle J C, Alderson D L, Li L 2005 PNAS 102 14497
[5] Wang X F, Chen G R 2002 Physica A 310 521
[6] Kocarev L, Amato P 2005 Chaos 15 024101
[7] Zhou J, Chen T 2006 IEEE Trans. Circuits Syst. I 53 733
[8] Tu L L, Lu J A 2009 Comput. Math. Appl. 57 28
[9] Zhang Q J, Lu J A, L J H 2008 IEEE Trans. Circuits Syst. II 55 183
[10] Liu J L 2013 Acta Phys. Sin. 62 040503 (in Chinese) [刘金良 2013 物理学报 62 040503]
[11] Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 物理学报 62 018901]
[12] Aldana M, Ballezaa E, Kauffmanb S, Resendiz O 2007 J. Theor. Biol. 245 433
[13] Liang J L, Wang Z D, Liu X H 2008 Nonlinear Dyn. 53 153
[14] Park J H, Lee S M, Jung H Y 2009 J. Optim. Theory Appl. 143 357
[15] Li H J, Yue D 2010 J. Phys. A: Math. Theor. 43 105101
[16] Li Z K, Duan Z S, Chen G R 2009 Chin. Phys. B 18 5228
[17] Ke C, Wang Z M, Tu L L 2013 Acta Phys. Sin. 62 010508 (in Chinese) [柯超, 王志明, 涂俐兰 2013 物理学报 62 010508]
[18] Wei R, Wang X Y 2004 Acta Phys. Sin. 53 3298 (in Chinese) [魏荣, 王行愚 2004 物理学报 53 3298]
[19] Wang Z Y, Huang L H, Zuo Y, Zhang L L 2010 Int. J. Control Automat. Syst. 8 266
[20] Lin T C, Kuo C H 2011 ISA Trans. 50 548
[21] Ahn C K, Jung S T, Kang S K, Joo S C 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 2168
[22] Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM)
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