Common Lyapunov functions for families of commuting nonlinear systems

Systems and Control Letters

Volumn 54, Issue 5, 2005, Pages 405-416

  Vu, Linh ^a   Liberzon, Daniel ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Common Lyapunov functions; Commutativity; Switched nonlinear systems; Uniform asymptotic stability

Indexed keywords

ASYMPTOTIC STABILITY; CONTROL SYSTEM ANALYSIS; INTEGRAL EQUATIONS; NONLINEAR SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; SYSTEM STABILITY; THEOREM PROVING; VECTORS;

COMMON LYAPUNOV FUNCTIONS; COMMUTATIVITY; SWITCHED NONLINEAR SYSTEMS; UNIFORM ASYMPTOTIC STABILITY;

LYAPUNOV METHODS;

EID: 15844419019     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2004.09.006     Document Type: Article

References (20)

1. A.A. Agrachev, and D. Liberzon Lie-algebraic stability criteria for switched systems SIAM J. Control Optim. 40 2001 253 269
2. D. Angeli, D. Liberzon, A note on uniform global asymptotic stability of switched systems in triangular form, in: Proceedings of the 14th International Symposium on Mathematical Theory of Networks and Systems, June 2000.
3. W.P. Dayawansa, and C.F. Martin A converse Lyapunov theorem for a class of dynamical systems which undergo switching, IEEE Trans. Automat. Control 44 1999 751 764
4. R.A. DeCarlo, M.S. Branicky, S. Petterson, and B. Lennartson Perspectives and results on the stability and stabilizability of hybrid systems Proc. IEEE 88 2000 1069 1082
5. H. Khalil Nonlinear Systems third ed. 2002 Prentice-Hall New Jersey
6. J. Kurzweil On the inversion of Lyapunov's second theorem on stability of motion Amer. Math. Soc. Translations 24 1956 19 77
7. D. Liberzon Switching in Systems and Control 2003 Birkhäuser Boston
8. D. Liberzon, J. Hespanha, and A.S. Morse Stability of switched systems a Lie-algebraic condition Systems Control Lett. 37 1999 117 122
9. D. Liberzon, and A.S. Morse Basic problems in stability and design of switched systems IEEE Control System Mag. 19 5 1999 57 70
10. Y. Lin, E.D. Sontag, and Y. Wang A smooth converse Lyapunov theorem for robust stability SIAM J. Control Optim. 34 1 1996 124 160
11. J.L. Mancilla-Aguilar A condition for the stability of switched nonlinear systems IEEE Trans. Automat. Control 45 11 2000 2077 2079
12. J.L. Mancilla-Aguilar, and R.A. Garcia A converse Lyapunov theorem for nonlinear switched systems Systems Control Lett. 41 1 2000 67 71
13. J.E. Marsden, and M.J. Hoffman Elementary is Classical Analysis second ed. 1993 Freeman and Co. New York
14. J.L. Massera On Liapounoff's conditions of stability Ann. Math. 50 3 1949 705 721
15. A.M. Meilakhs Design of stable control systems subject to parametric perturbation Automat. Remote Control 39 1978 1409 1418
16. Y. Mori, T. Mori, Y. Kuroe, On a class of linear constant systems which have a common quadratic Lyapunov function, in: Proceedings of the 37th IEEE Conference on Decision and Control, vol. 3, December 1998, pp. 2808-2809.
17. K.S. Narendra, and J. Balakrishnan A common Lyapunov function for stable LTI system with commuting A-matrices IEEE Trans. Automat. Control 39 12 1994 2469 2471
18. H. Shim, D.J. Noh, J.H. Seo, Common Lyapunov function for exponentially stable nonlinear systems, Presented at the 4th SIAM Conference on Control and its Applications, Florida, 1998.
19. R.N. Shorten, K.S. Narendra, On the stability and existence of common Lyapunov functions for stable linear switching systems, in: Proceedings of the 37th IEEE Conference on Decision and Control, 1998, pp. 3723-3724.
20. F.W. Wilson Smoothing derivatives of functions and applications Trans. Amer. Math. Soc. 139 1969 413 428