A condition for the stability of switched nonlinear systems

IEEE Transactions on Automatic Control

Volumn 45, Issue 11, 2000, Pages 2077-2079

  Mancilla Aguilar, J L ^a  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

Hybrid systems; Lyapunov stability; Nonlinear; Switched systems

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; INTELLIGENT CONTROL; LYAPUNOV METHODS; NONLINEAR CONTROL SYSTEMS; SWITCHING SYSTEMS; VECTORS;

LIE BRACKET; LIPSCHITZ VECTOR FIELDS; PAIRWISE COMMUTATION; SWITCHED NONLINEAR SYSTEMS;

CONTROL SYSTEM ANALYSIS;

EID: 0034315065     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.887629     Document Type: Article

References (16)

1. A. A. Agrachev and D. Liberzon, "Lie-algebraic conditions for exponential stability of switched systems," in Proc. 38th Conf. Decision and Control, Phoenix, AZ, 1999, pp. 2679-2684.
2. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994, vol. 15, Studies in Applied Mathematics.
3. W. P. Dayawansa and C. F. Martin, "A converse Lyapunov theorem for a class of dynamical system which undergo switching," IEEE Trans. Automat. Contr., vol. 44, pp. 751-760, 1999.
4. W. Hahn, Stability of Motion. Berlin, Germany: Springer-Verlag, 1967.
5. D. Liberzon and A. S. Morse, "Basic problems in stability and design of switched systems," IEEE Contr. Syst. Mag., vol. 19, pp. 59-70, 1999.
6. D. Liberzon, J. P. Hespanha, and A. S. Morse, "Stability of switched systems: A Lie-algebraic condition," Syst. Contr. Lett., vol. 37, pp. 117-122, 1999.
7. Y. Lin, E. D. Sontag, and Y. Wang, "A smooth converse Lyapunov theorem for robust stability," SIAM J. Contr. Optim., vol. 34, pp. 124-160, 1996.
8. H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems. New York: Springer-Verlag, 1990.
9. J. L. Mancilla-Aguilar and R. A. Garcìa, "A converse Lyapunov theorem for nonlinear switched systems," Syst. Contr. Lett., vol. 44, pp. 67-71, 2000.
10. Y. Mori, T. Mori, and Y. Kuroe, "A solution to the common Lyapunov function problem for continuous-time systems," in Proc. 36th Conf. Decision and Control, San Diego, CA, 1997, pp. 3530-3531.
11. K. S. Narendra and J. Balakrishnan, "A common Lyapunov function for stable LTI systems with commuting A-matrices," IEEE Trans Automat. Contr., vol. 39, pp. 2469-2471, 1994.
12. T. Ooba and Y. Funahashi, "On a common quadratic Lyapunov function for widely distant systems," IEEE Trans Automat. Contr., vol. 42, pp. 1697-1699, 1997.
13. H. Shim, D. J. Noh, and J. H. Seo, "Common Lyapunov function for exponentially stable nonlinear systems," in 4th SIAM Conf. Control and its Applications, Jacksonville, FL, 1998.
14. R. N. Shorten and K. S. Narendra, "A sufficient condition for the existence of a common Lyapunov function for two second-order linear systems," in Proc. 36th Conf. Decision and Control, San Diego, CA, 1997, pp. 3521-3522.
15. R. N. Shorten and K. S. Narendra, "On the existence of a common Lyapunov for linear stable switching systems," in Proc. 10th Yale Workshop Adaptive and Learning Systems, 1998, pp. 130-140.
16. E. D. Sontag, "Comments on integral variants of ISS," Syst. Contr. Lett., vol. 34, pp. 93-100, 1998.