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Dynamical behavior of networks of nonuniform Timoshenko beams system with boundary timedelay inputs
Consensus and synchronization in discretetime networks of multiagents with stochastically switching topologies and time delays
1.  Center for Computational Systems Biology, Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433 
2.  Max Planck Institute for Mathematics in theSciences, Inselstr. 22, 04103 Leipzig, Germany 
References:
[1] 
P.A. Bliman and G. FerrariTrecate, Average consensus problems in networks of agents with delayed communications, Automatica, 44 (2008), 19851995. doi: 10.1016/j.automatica.2007.12.010. 
[2] 
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: A graphical approach, SIAM J. Control Optim., 47 (2008), 575600. doi: 10.1137/060657005. 
[3] 
S. Chatterjee and E. Seneta, Towards consensus: Some convergence theorems on repeated averaging, J. Appl. Prob., 14 (1977), 8997. doi: 10.2307/3213262. 
[4] 
O. Chilina, "fUniform Ergodicity of Markov Chains,'' Supervised Project, Unversity of Toronto, 2006. 
[5] 
M. H. DeGroot, Reaching a consensus, J. Amer. Statist. Assoc., 69 (1974), 118121. doi: 10.2307/2285509. 
[6] 
D. V. Dimarogonasa and K. H. Johansson, Stability analysis for multiagent systems using the incidence matrix: Quantized communication and formation control, Automatica, 46 (2010), 695700. doi: 10.1016/j.automatica.2010.01.012. 
[7] 
R. Durrett, "Probability: Theory and Examples," 3^{rd} edition, Belmont, CA: Duxbury Press, 2005. 
[8] 
F. Fagnani and S. Zampieri, Average consensus with packet drop communication, SIAM J. Control Optim., 48 (2009), 102133. doi: 10.1137/060676866. 
[9] 
L. Fang, P. J. Antsaklis and A. Tzimas, Asynchronous consensus protocols: Preliminary results, simulations and open questions, Proceedings of the 44th IEEE Conf. Decision and Control, the Europ. Control Conference (2005), 21942199. 
[10] 
J. A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formations, IEEE Trans. Autom. Control, 49 (2004), 14651476. doi: 10.1109/TAC.2004.834433. 
[11] 
C. Godsil and G. Royle, "Algebraic Graph Theory," SpringerVerlag, New York, 2001. 
[12] 
J. Hajnal, The ergodic properties of nonhomogeneous finite Markov chains, Proc. Camb. Phil. Soc., 52 (1956), 6777. doi: 10.1017/S0305004100030991. 
[13] 
J. Hajnal, Weak ergodicity in nonhomogeneous Markov chains, Proc. Camb. Phil. Soc., 54 (1958), 233246. doi: 10.1017/S0305004100033399. 
[14] 
Y. Hatano and M. Mesbahi, Agreement over random networks, IEEE Trans. Autom. Control, 50 (2005), 18671872. doi: 10.1109/TAC.2005.858670. 
[15] 
R. A. Horn and C. R. Johnson, "Matrix Analysis," Cambridge University Press, 1985. 
[16] 
Y. Kuramoto, "Chemical Oscillations, Waves, And Turbulence," SpringerVerlag, New York, 1984. 
[17] 
J. Lin, A. S. Morse and B. D. O. Anderson, The multiagent rendezvous problem Part 2: The asynchronous case, SIAM J. Control Optim., 46 (2007), 21202147. doi: 10.1137/040620564. 
[18] 
B. Liu, W. Lu and T. Chen, Consensus in networks of multiagents with switching topologies modeled as adapted stochastic processes, SIAM J. Control Optim., 49 (2011), 227253. doi: 10.1137/090745945. 
[19] 
W. Lu, F. M. Atay and J. Jost, Synchronization of discretetime networks with timevarying couplings, SIAM J. Math. Analys., 39 (2007), 12311259. doi: 10.1137/060657935. 
[20] 
W. Lu, F. M. Atay and J. Jost, Chaos synchronization in networks of coupled maps with timevarying topologies, Eur. Phys. J. B, 63 (2008), 399406. doi: 10.1140/epjb/e2008000233. 
[21] 
N. A. Lynch, "Distributed Algorithms," CA: Morgan Kaufmann, San Francisco, 1996. 
[22] 
W. Ni and D. Z. Cheng, Leaderfollowing consensus of multiagent systems under fixed and switching topologies, Systems & Control Letters, 59 (2010), 209217. doi: 10.1016/j.sysconle.2010.01.006. 
[23] 
W. Michiels, C.I. Morărescu and S.I. Niculescu, Consensus problems with distributed delays, with application to traffic flow models, SIAM J. Control Optim., 48 (2009), 77101. doi: 10.1137/060671425. 
[24] 
L. Moreau, Stability of continuoustime distributed consensus algorithms, 43rd IEEE Conference on Decision and Control, 4 (2004), 39984003. 
[25] 
L. Moreau, Stability of multiagent systems with timedependent communication links, IEEE Trans. Autom. Control, 50 (2005), 169182. doi: 10.1109/TAC.2004.841888. 
[26] 
R. OlfatiSaber and J. S. Shamma, Consensus filters for sensor networks and distributed sensor fusion, 44th IEEE Conference on Decision and Control 2005, and 2005 European Control Conference CDCECC '05. 66986703. doi: 10.1109/CDC.2005.1583238. 
[27] 
R. OlfatiSaber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multiagent systems, Proceedings of the IEEE, 95 (2007), 215233. doi: 10.1109/JPROC.2006.887293. 
[28] 
R. OlfatiSaber and R. M. Murray, Consensus problems in networks of agents with switching topology and timedelays, IEEE Trans. Autom. Control, 49 (2004), 15201533. doi: 10.1109/TAC.2004.834113. 
[29] 
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge University Press, 2001. doi: 10.1017/CBO9780511755743. 
[30] 
J. Shen, A geometric approach to ergodic nonhomogeneous Markov chains, Wavelet Anal. Multi. Meth., LNPAM, 212 (2000), 341366. 
[31] 
A. TahbazSalehi and A. Jadbabaie, A necessary and sufficient condition for consensus over random networks, IEEE Trans. Autom. Control, 53 (2008), 791795. doi: 10.1109/TAC.2008.917743. 
[32] 
T. Vicsek, A. Czirók, E. BenJacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of selfdriven particles, Phys. Rev. Lett., 75 (1995), 12261229. doi: 10.1103/PhysRevLett.75.1226. 
[33] 
A. T. Winfree, "The Geometry of Biological Time," Springer Verlag, New York, 1980. 
[34] 
J. Wolfowitz, Products of indecomposable, aperiodic, stochastic matrices, Proceedings of AMS, 14 (1963), 733737. 
[35] 
C. W. Wu, Synchronization and convergence of linear dynamics in random directed networks, IEEE Trans. Autom. Control, 51 (2006), 12071210. 
[36] 
F. Xiao and L. Wang, Consensus protocols for discretetime multiagent systems with timevarying delays, Automatica, 44 (2008), 25772582. 
[37] 
F. Xiao and L. Wang, Asynchronous consensus in continuoustime multiagent systems with switching topology and timevarying delays, IEEE Transactions on Automatic Control, 53 (2008), 18041816. 
[38] 
Y. Zhang and Y.P. Tian, Consentability and protocol design of multiagent systems with stochastic switching topology, Automatica, 45 (2009), 11951201. 
show all references
References:
[1] 
P.A. Bliman and G. FerrariTrecate, Average consensus problems in networks of agents with delayed communications, Automatica, 44 (2008), 19851995. doi: 10.1016/j.automatica.2007.12.010. 
[2] 
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: A graphical approach, SIAM J. Control Optim., 47 (2008), 575600. doi: 10.1137/060657005. 
[3] 
S. Chatterjee and E. Seneta, Towards consensus: Some convergence theorems on repeated averaging, J. Appl. Prob., 14 (1977), 8997. doi: 10.2307/3213262. 
[4] 
O. Chilina, "fUniform Ergodicity of Markov Chains,'' Supervised Project, Unversity of Toronto, 2006. 
[5] 
M. H. DeGroot, Reaching a consensus, J. Amer. Statist. Assoc., 69 (1974), 118121. doi: 10.2307/2285509. 
[6] 
D. V. Dimarogonasa and K. H. Johansson, Stability analysis for multiagent systems using the incidence matrix: Quantized communication and formation control, Automatica, 46 (2010), 695700. doi: 10.1016/j.automatica.2010.01.012. 
[7] 
R. Durrett, "Probability: Theory and Examples," 3^{rd} edition, Belmont, CA: Duxbury Press, 2005. 
[8] 
F. Fagnani and S. Zampieri, Average consensus with packet drop communication, SIAM J. Control Optim., 48 (2009), 102133. doi: 10.1137/060676866. 
[9] 
L. Fang, P. J. Antsaklis and A. Tzimas, Asynchronous consensus protocols: Preliminary results, simulations and open questions, Proceedings of the 44th IEEE Conf. Decision and Control, the Europ. Control Conference (2005), 21942199. 
[10] 
J. A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formations, IEEE Trans. Autom. Control, 49 (2004), 14651476. doi: 10.1109/TAC.2004.834433. 
[11] 
C. Godsil and G. Royle, "Algebraic Graph Theory," SpringerVerlag, New York, 2001. 
[12] 
J. Hajnal, The ergodic properties of nonhomogeneous finite Markov chains, Proc. Camb. Phil. Soc., 52 (1956), 6777. doi: 10.1017/S0305004100030991. 
[13] 
J. Hajnal, Weak ergodicity in nonhomogeneous Markov chains, Proc. Camb. Phil. Soc., 54 (1958), 233246. doi: 10.1017/S0305004100033399. 
[14] 
Y. Hatano and M. Mesbahi, Agreement over random networks, IEEE Trans. Autom. Control, 50 (2005), 18671872. doi: 10.1109/TAC.2005.858670. 
[15] 
R. A. Horn and C. R. Johnson, "Matrix Analysis," Cambridge University Press, 1985. 
[16] 
Y. Kuramoto, "Chemical Oscillations, Waves, And Turbulence," SpringerVerlag, New York, 1984. 
[17] 
J. Lin, A. S. Morse and B. D. O. Anderson, The multiagent rendezvous problem Part 2: The asynchronous case, SIAM J. Control Optim., 46 (2007), 21202147. doi: 10.1137/040620564. 
[18] 
B. Liu, W. Lu and T. Chen, Consensus in networks of multiagents with switching topologies modeled as adapted stochastic processes, SIAM J. Control Optim., 49 (2011), 227253. doi: 10.1137/090745945. 
[19] 
W. Lu, F. M. Atay and J. Jost, Synchronization of discretetime networks with timevarying couplings, SIAM J. Math. Analys., 39 (2007), 12311259. doi: 10.1137/060657935. 
[20] 
W. Lu, F. M. Atay and J. Jost, Chaos synchronization in networks of coupled maps with timevarying topologies, Eur. Phys. J. B, 63 (2008), 399406. doi: 10.1140/epjb/e2008000233. 
[21] 
N. A. Lynch, "Distributed Algorithms," CA: Morgan Kaufmann, San Francisco, 1996. 
[22] 
W. Ni and D. Z. Cheng, Leaderfollowing consensus of multiagent systems under fixed and switching topologies, Systems & Control Letters, 59 (2010), 209217. doi: 10.1016/j.sysconle.2010.01.006. 
[23] 
W. Michiels, C.I. Morărescu and S.I. Niculescu, Consensus problems with distributed delays, with application to traffic flow models, SIAM J. Control Optim., 48 (2009), 77101. doi: 10.1137/060671425. 
[24] 
L. Moreau, Stability of continuoustime distributed consensus algorithms, 43rd IEEE Conference on Decision and Control, 4 (2004), 39984003. 
[25] 
L. Moreau, Stability of multiagent systems with timedependent communication links, IEEE Trans. Autom. Control, 50 (2005), 169182. doi: 10.1109/TAC.2004.841888. 
[26] 
R. OlfatiSaber and J. S. Shamma, Consensus filters for sensor networks and distributed sensor fusion, 44th IEEE Conference on Decision and Control 2005, and 2005 European Control Conference CDCECC '05. 66986703. doi: 10.1109/CDC.2005.1583238. 
[27] 
R. OlfatiSaber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multiagent systems, Proceedings of the IEEE, 95 (2007), 215233. doi: 10.1109/JPROC.2006.887293. 
[28] 
R. OlfatiSaber and R. M. Murray, Consensus problems in networks of agents with switching topology and timedelays, IEEE Trans. Autom. Control, 49 (2004), 15201533. doi: 10.1109/TAC.2004.834113. 
[29] 
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge University Press, 2001. doi: 10.1017/CBO9780511755743. 
[30] 
J. Shen, A geometric approach to ergodic nonhomogeneous Markov chains, Wavelet Anal. Multi. Meth., LNPAM, 212 (2000), 341366. 
[31] 
A. TahbazSalehi and A. Jadbabaie, A necessary and sufficient condition for consensus over random networks, IEEE Trans. Autom. Control, 53 (2008), 791795. doi: 10.1109/TAC.2008.917743. 
[32] 
T. Vicsek, A. Czirók, E. BenJacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of selfdriven particles, Phys. Rev. Lett., 75 (1995), 12261229. doi: 10.1103/PhysRevLett.75.1226. 
[33] 
A. T. Winfree, "The Geometry of Biological Time," Springer Verlag, New York, 1980. 
[34] 
J. Wolfowitz, Products of indecomposable, aperiodic, stochastic matrices, Proceedings of AMS, 14 (1963), 733737. 
[35] 
C. W. Wu, Synchronization and convergence of linear dynamics in random directed networks, IEEE Trans. Autom. Control, 51 (2006), 12071210. 
[36] 
F. Xiao and L. Wang, Consensus protocols for discretetime multiagent systems with timevarying delays, Automatica, 44 (2008), 25772582. 
[37] 
F. Xiao and L. Wang, Asynchronous consensus in continuoustime multiagent systems with switching topology and timevarying delays, IEEE Transactions on Automatic Control, 53 (2008), 18041816. 
[38] 
Y. Zhang and Y.P. Tian, Consentability and protocol design of multiagent systems with stochastic switching topology, Automatica, 45 (2009), 11951201. 
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