Stabilization of switched linear systems via LaSalle's invariance principle

2007 IEEE International Conference on Control and Automation, ICCA

Volumn , Issue , 2007, Pages 1-6

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

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

INVARIANCE; LYAPUNOV FUNCTIONS; MULTI AGENT SYSTEMS; SWITCHING NETWORKS;

LASALLE'S INVARIANCE PRINCIPLE; SWITCHING MODES;

LINEAR SYSTEMS;

EID: 44349189335     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCA.2007.4376308     Document Type: Conference Paper

References (17)

1. A.A. Agrachev, D. Liberzon, Lie-algebraic stability criteria for switched systems, SIAM J. Contr. Opt., Vol. 40, No. 1, pp. 253-269, 2001.
2. A. Bacciotti, L. Mazzi, An invariace principle for nonlinear switched systems, Sys. Contr. Lett., Vol. 54, pp. 1109-1119, 2005.
3. D. Cheng, L. Guo and J. Huang, On quatratic Lyapunov function, IEEE Trans. Aut. Contr., Vol.48, No.5, pp.885-890, 2003.
4. D. Cheng, J. Wang, X. Hu, LaSalle's Invariance Principle of Switched Linear Systems and its Application to Consensus of Multi-agent Systems, submitted for pub.
5. W.P. Dayawansa, C.F. Martin, A converse Lyapunov theorem for a class of dynamic systems which undergo switching, IEEE Trans. Aut. Contr., Vol.44, No.?, pp.751-760, 1999.
6. J.P. Hespanha, Uniform stability of switched linear sysems: Extensions of LaSalle's Invariance Principle, IEEE Trans. Aut. Contr., Vol. 49, pp. 470-482, 2004.
7. J.P. Hespanha, D. Liberzon, E. Angeli, E.D. Sontag, Nonlinear observability notion and stability of switched systems, IEEE Trans. Aut. Contr., Vol. 50, pp. 154-168, 2005.
8. D. Liberzon, J.P. Hespanha, and A.S. Morse, Stability of switched systems: a Lie-algebraic condi- tion, Sys. Contr. Lett., Vol. 37, No. 3, pp. 117-122, 1999.
9. J.L. Mancilla-Aguilar, R.A. Garcia, A converse Lyapunov theorem for nonlinear switched systems, Sys. Contr. Lett., Vol. 41, pp 67-71, 2000.
10. J.L. Mancilla-Aguilar, R.A. Garcia, An extension of LaSalle's invariance principle for switched systems, Sys. Contr. Lett., Vol. 55, pp 376-384, 2006.
11. W.J. Rugh, Linear Systems Theory, Upper Saddle River, NJ, Prentice-Hall, 1993.
12. R.N. Shorten, K.S. Narendra, O. Mason, A result on common quadratic Lyapunov functions, IEEE Trans. Aut. Contr., Vol. 48, No. 1, pp. 618-621, 2003.
13. C. Godsil and G. Royle, Algebraic Graph Theory, New York: Springer-Verlag, 2001.
14. Y. Hong, J. Hu, and L. Gao, Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, Vol.42, No.7, pp. 1177-1182 (2006).
15. Y. Hong, L. Gao, D. Cheng and J. Hu, Coordination of multi-agent systems with varying interconnection topology using common Lyapunov function, submitted to IEEE Trans. Automatic Control.
16. R. Horn and C. Johnson, Matrix Analysis, New York: Cambbridge Univ. Press, 1985.
17. A. Jadbabaie, J. Lin, and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automatic Control, Vol.48, No.6, pp.998-1001(2003).