zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Leader-following consensus in networks of agents with nonuniform time-varying delays. (English) Zbl 1264.93007
Summary: We are concerned with a leader-following consensus problem for networks of agents with fixed and switching topologies as well as nonuniform time-varying communication delays. By employing Lyapunov-Razumikhin function, a necessary and sufficient condition is derived in the case of fixed topology, and a sufficient condition is obtained in the case when the interconnection topology is switched and satisfies certain condition. Simulation results are provided to illustrate the theoretical results.

MSC:
93A13Hierarchical systems
93D15Stabilization of systems by feedback
34D06Synchronization
34K20Stability theory of functional-differential equations
WorldCat.org
Full Text: DOI
References:
[1] R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215-233, 2007. · doi:10.1109/JPROC.2006.887293
[2] R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520-1533, 2004. · doi:10.1109/TAC.2004.834113
[3] T. Vicsek, A. Czirk, E. Ben-Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,” Physical Review Letters, vol. 75, no. 6, pp. 1226-1229, 1995. · doi:10.1103/PhysRevLett.75.1226
[4] A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988-1001, 2003. · doi:10.1109/TAC.2003.812781
[5] Y. G. Sun, L. Wang, and G. Xie, “Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays,” Systems & Control Letters, vol. 57, no. 2, pp. 175-183, 2008. · Zbl 1133.68412 · doi:10.1016/j.sysconle.2007.08.009
[6] P.-A. Bliman and G. Ferrari-Trecate, “Average consensus problems in networks of agents with delayed communications,” Automatica, vol. 44, no. 8, pp. 1985-1995, 2008. · Zbl 1283.93013 · doi:10.1016/j.automatica.2007.12.010
[7] Y. G. Sun and L. Wang, “Consensus problems in networks of agents with double-integrator dynamics and time-varying delays,” International Journal of Control, vol. 82, no. 10, pp. 1937-1945, 2009. · Zbl 1178.93013 · doi:10.1080/00207170902838269
[8] Y. G. Sun and L. Wang, “Consensus of multi-agent systems in directed networks with uniform time-varying delays,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1607-1613, 2009. · doi:10.1109/TAC.2009.2017963
[9] P. Lin and Y. Jia, “Average consensus in networks of multi-agents with both switching topology and coupling time-delay,” Physica A, vol. 387, no. 1, pp. 303-313, 2008. · doi:10.1016/j.physa.2007.08.040
[10] P. Lin and Y. Jia, “Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies,” IEEE Transactions on Automatic Control, vol. 55, no. 3, pp. 778-784, 2010. · doi:10.1109/TAC.2010.2040500
[11] J. Hu and Y. Hong, “Leader-following coordination of multi-agent systems with coupling time delays,” Physica A, vol. 374, no. 2, pp. 853-863, 2007. · doi:10.1016/j.physa.2006.08.015
[12] J. Hu and Y. S. Lin, “Consensus control for multi-agent systems with double-integrator dynamics and time delays,” IET Control Theory & Applications, vol. 4, no. 1, pp. 109-118, 2010. · doi:10.1049/iet-cta.2008.0479
[13] W. Zhu and D. Cheng, “Leader-following consensus of second-order agents with multiple time-varying delays,” Automatica, vol. 46, no. 12, pp. 1994-1999, 2010. · Zbl 1205.93056 · doi:10.1016/j.automatica.2010.08.003
[14] W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655-661, 2005. · doi:10.1109/TAC.2005.846556
[15] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99, Springer, New York, NY, USA, 1993. · Zbl 0787.34002
[16] K. Gu, V. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Birkhauser, 2003.
[17] P. C. Parks and V. Hahn, Stability Theory, Prentice Hall, Upper Saddle River, NJ, USA, 1992.
[18] Y. Cao, W. Ren, and Y. Li, “Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication,” Automatica, vol. 45, no. 5, pp. 1299-1305, 2009. · Zbl 1162.93004 · doi:10.1016/j.automatica.2009.01.018
[19] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, NY, USA, 1994. · Zbl 0801.15001
[20] Z.-J. Tang, T.-Z. Huang, J.-L. Shao, and J.-P. Hu, “Leader-following consensus for multi-agent systems via sampled-data control,” IET Control Theory & Applications, vol. 5, no. 14, pp. 1658-1665, 2011. · doi:10.1049/iet-cta.2010.0653
[21] K. Peng and Y. Yang, “Leader-following consensus problem with a varying-velocity leader and time-varying delays,” Physica A, vol. 388, no. 2-3, pp. 193-208, 2009. · doi:10.1016/j.physa.2008.10.009
[22] J. Hu and G. Feng, “Distributed tracking control of leader-follower multi-agent systems under noisy measurement,” Automatica, vol. 46, no. 8, pp. 1382-1387, 2010. · Zbl 1204.93011 · doi:10.1016/j.automatica.2010.05.020
[23] Y. Sun, D. Zhao, and J. Ruan, “Consensus in noisy environments with switching topology and time-varying delays,” Physica A, vol. 389, no. 19, pp. 4149-4161, 2010. · doi:10.1016/j.physa.2010.05.038
[24] D. Cheng, J. Wang, and X. Hu, “An extension of LaSalle’s invariance principle and its application to multi-agent consensus,” IEEE Transactions on Automatic Control, vol. 53, no. 7, pp. 1765-1770, 2008. · doi:10.1109/TAC.2008.928332
[25] L. Moreau, “Stability of multiagent systems with time-dependent communication links,” IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 169-182, 2005. · doi:10.1109/TAC.2004.841888
[26] W. Ren and E. Atkins, “Distributed multi-vehicle coordinated control via local information exchange,” International Journal of Robust and Nonlinear Control, vol. 17, no. 10-11, pp. 1002-1033, 2007. · Zbl 1266.93010 · doi:10.1002/rnc.1147