On the nonexistence of quadratic lyapunov functions for consensus algorithms

IEEE Transactions on Automatic Control

Volumn 53, Issue 11, 2008, Pages 2642-2645

  Olshevsky, Alex ^a   Tsitsiklis, John N ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Consensus algorithms; Multi agent systems; Multi agent systems

Indexed keywords

DIFFERENTIAL EQUATIONS; ELECTRIC POWER TRANSMISSION NETWORKS; FUNCTIONS; LYAPUNOV FUNCTIONS; PROBABILITY DENSITY FUNCTION; TELECOMMUNICATION NETWORKS;

CONSENSUS ALGORITHMS; QUADRATIC LYAPUNOV FUNCTIONS; SUFFICIENT CONDITIONS;

MULTI AGENT SYSTEMS;

EID: 58249126992     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.2007878     Document Type: Article

References (12)

1. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods. Englewood Cliffs, NJ: Prentice Hall, 1989.
2. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-Dynamic Programming. Nashua, NH: Athena Scientific, 1996.
3. V. D. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Tsitsiklis, "Convergence in multiagent coordination, consensus, and flocking," in Proc. Joint 44th IEEE Conf. Decision Control (CDC'05), Seville, Spain, Dec. 2005, pp. 2996-3000.
4. M. Cao, A. S. Morse, and B. D. O. Anderson, "Coordination of an asynchronous, multi-agent system via averaging," in Proc. 16th Int. Fed. Automat. Control World Congress (IFAC'05), Prague, Czech Republic, Jul. 2005, CD ROM.
5. J. M. Hendrickx and V. D. Blondel, "Convergence of different linear and non-linear Vicsek models," in Proc. 17th Int. Symp. Math. Theory Networks Syst. (MTNS'06), Kyoto, Japan, Jul. 2006, pp. 1229-1240.
6. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Automat. Control, vol. 48, no. 3, pp. 988-1001, Mar. 2003.
7. S. Li and H. Wang, "Multi-Agent Coordination Using Nearest-Neighbor Rules: Revisiting the Vicsek Model," in [Online]H Available: http:// arxiv.org/abs/cs.MA/0407021 2008
8. D. Liberzon and A. S. Morse, "Basic problems in stability and design of switched systems," IEEE Control Syst. Mag., vol. 19, no. 5, pp. 59-70, Oct. 1999.
9. L. Moreau, "Stability of multiagent systems with time-dependent communication links," IEEE Trans. Automat. Control, vol. 50, no. 2, pp. 169-182, Feb. 2005.
10. J. N. Tsitsiklis, "Problems in Decentralized Decision Making and Computation" Ph.D. dissertation, Dept. Elect. Eng. Comp. Sci., Mass. Inst. Technol., Cambridge, 1984 [Online]. Available: http:// hdl.handle.net/1721.1/15254
11. J. N. Tsitsiklis, D. P. Bertsekas, and M. Athans, "Distributed asynchronous deterministic and stochastic gradient optimization algorithms," IEEE Trans. Automat. Control, vol. AC-31, no. 9, pp. 803-812, Sep. 1986.
12. T. Vicsek, E. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, "Novel type of phase transitions in a system of self-driven particles," Phys. Rev. Lett., vol. 75, pp. 1226-1229, 1995.