An extension of LaSalle's invariance principle and its application to multi-agent consensus

IEEE Transactions on Automatic Control

Volumn 53, Issue 7, 2008, Pages 1765-1770

  Cheng, Daizhan ^a   Wang, Jinhuan ^a   Hu, Xiaoming ^b  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

LaSalle's invariance principle; Multi agent consensus; Switched linear systems; Weak common quadratic Lyapunov function

Indexed keywords

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; CONTROL THEORY; LINEAR SYSTEMS;

ASYMPTOTICALLY STABLE; CONSENSUS PROBLEMS; DOUBLE INTEGRATOR; ERGODICITY; GLOBAL ASYMPTOTIC STABILITY; LASALLE'S INVARIANCE PRINCIPLE; LYAPUNOV; MULTI AGENTS; MULTI-AGENT CONSENSUS; SWITCHED LINEAR SYSTEMS; SWITCHING MODES; WEAK COMMON QUADRATIC LYAPUNOV FUNCTION;

MULTI AGENT SYSTEMS;

EID: 52249114264     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.928332     Document Type: Article

References (19)

1. A. Bacciotti and L. Mazzi, "An invariance principle for nonlinear switched systems," Syst. Control Lett., vol. 54, pp. 1109-1119, 2005.
2. M. Branicky, "Multiple Lyapunov functions and other analysis tools for switched and hybrid systems," IEEE Trans. Automat. Control, vol. 43, no. 4, pp. 475-482, Apr. 1998.
3. D. Cheng, L. Guo, and J. Huang, "On quadratic Lyapunov function," IEEE Trans. Automat. Control, vol. 48, no. 5, pp. 885-890, May 2003.
4. V. Chellaboina, S. P. Bhat, and W. M. Haddad, "An invariance principle for nonlinear hybrid and impulsive dynamical systems," Nonlin. Anal. vol. 53, pp. 527-550, 2003.
5. R. G. Sanfelice, R. Goebel, and A. R. Teel, "Results on convergence in hybrid systems via detectability and on invariance principle," in Proc. 24th IEEE ACC, 2005, pp. 551-556.
6. R. N. Shorten, K. S. Narendra, and O. Mason, "A result on common quadratic Lyapunov functions," IEEE Trans. Automat. Control, vol. 48, no. 1, pp. 618-621, Jan. 2003.
7. W. P. Dayawansa and C. F. Martin, "A converse Lyapunov theorem for a class of dynamic systems which undergo switching," IEEE Trans. Automat. Control, vol. 44, no. 4, pp. 751-760, Apr. 1999.
8. J. P. Hespanha, "Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle," IEEE Trans. Automat. Control, vol. 49, no. 4, pp. 470-482, Apr. 2004.
9. J. P. Hespanha, D. Liberzon, E. Anglei, and E. D. Sontag, "Nonlinear observability notion and stability of switched systems," IEEE Trans. Automat. Control, vol. 50, no. 2, pp. 154-168, Feb. 2005.
10. D. Liberzon, J. P. Hespanha, and A. S. Morse, "Stability of switched systems: A Lie-algebraic condition," Syst. Control Lett., vol. 37, no. 3, pp. 117-122, 1999.
11. J. L. Mancilla-Aguilar and R. A. Garcia, "An extension of LaSalle's invaiiance principle for switched systems," Syst. Control Lett., vol. 55, pp. 376-384, 2006.
12. W. J. Rugh, Linear Systems Theory. Upper Saddle River, NJ: Prentice-Hall, 1993.
13. R. Horn and C. Johnson, Matrix Analysis. New York: Cambridge Univ. Press, 1985.
14. Y. Hong, L. Gao, D. Cheng, and J. Hu, "Coordination of multi-agent systems with varying interconnection topology using common Lyapunov function," IEEE Trans. Automat. Control, vol. 52, no. 5, pp. 943-948, May 2007.
15. 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. 6, pp. 998-1001, Jun. 2003.
16. L. Moreau, "Stability of multiagent systems with time-dependent communication links," IEEE Trans. Automat. Control, vol. 50, no. 2, pp. 169-182, Feb. 2005.
17. R. Olfati-Saber and R. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Trans. Automat. Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
18. W. Ren and R. W. Beard, "Consensus seeking in multi-agent systems using dynamically changing interaction topologies," IEEE Trans. Automat. Control, vol. 50, no. 5, pp. 655-561, May 2005.
19. C. Godsil and G. Royle, Algebraic Graph Theory. New York: Springer-Verlag, 2001.