Nonlinear norm-observability notions and stability of switched systems

IEEE Transactions on Automatic Control

Volumn 50, Issue 2, 2005, Pages 154-168

  Hespanha, João P ^a   Liberzon, Daniel ^b   Angeli, David ^c   Sontag, Eduardo D ^d  

^a University of California at Santa Barbara   (United States)

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

^c UNIVERSITY OF FLORENCE   (Italy)

^d RUTGERS UNIVERSITY   (United States)

Author keywords

LaSalle's stability theorem; Nonlinear system; Observability; Switched system

Indexed keywords

CONTROL SYSTEM ANALYSIS; LYAPUNOV METHODS; OBSERVABILITY; SYSTEM STABILITY;

LASALLE STABILITY THEOREM; SWITCHED SYSTEM;

NONLINEAR CONTROL SYSTEMS;

EID: 14644408071     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.841937     Document Type: Article

References (39)

1. D. Angeli, "A Lyapunov approach to incremental stability properties," IEEE Trans. Autom. Control, vol. 47, no. 3, pp. 410-422, Mar. 2002.
2. D. Angeli and E. Mosca, "Lyapunov-based switching supervisory control of nonlinear uncertain systems," IEEE Trans. Autom. Control, vol. 47, no. 3, pp. 500-505, Mar. 2002.
3. D. Angeli and E. Sontag, "Forward completeness, unboundedness observability, and their Lyapunov characterizations," Syst. Control Lett., vol. 38, pp. 209-217, 1999.
4. D. Angeli, E. Sontag, and Y. Wang, "A characterization of integral input-to-state stability," IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1082-1097, Jun. 2000.
5. Z. Artstein, "Stability, observability and invariance," J. Diff. Equat., vol. 44, pp. 224-248, 1982.
6. Z. Arstein, "Stabilization with relaxed controls," Nonlinear Anal. vol. 7, pp. 1163-1173, 1983.
7. E. A. Barbashin and N. N. Krasovskii, "On stability of motion in the large" (in Russian), Dokl. Akad. Nauk SSSR, vol. 86, pp. 453-456, 1952.
8. A. Bemporad, G. Ferrari-Trecate, and M. Morari, "Observability and controllability of piecewise affine and hybrid systems," IEEE Trans. Autom. Control, vol. 45, no. 10, pp. 1864-1876, Oct. 2000.
9. M. S. Branicky, "Multiple Lyapunov functions and other analysis tools for switched and hybrid systems," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 475-482, Apr. 1998.
10. R. W. Brockett, "On the stability of nonlinear feedback systems," IEEE Trans. Ind. Appl., vol. IA-83, pp. 443-449, 1964.
11. R. W. Brockett, "Asymptotic stability and feedback stabilization," in Differential Geometric Control Theory, R. W. Brockett, R. S. Millman, and H. J. Sussmann, Eds. Boston, MA: Birkhäuser, 1983, pp. 181-191.
12. R. A. DeCarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems," Proc. IEEE, vol. 88, no. 7, pp. 1069-1082, Jul. 2000.
13. S. Diop and M. Fliess, "Nonlinear observability, identifiability, and persistent trajectories," in Proc. 30th IEEE Conf. Decision and Control, 1991, pp. 714-719.
14. M. Fu and B. R. Barmish, "Adaptive stabilization of linear systems via switching control," IEEE Trans. Autom. Control, vol. AC-31, no. 12, pp. 1097-1103, Dec. 1986.
15. H. Hermes, "Large-time local controllability via homogeneous approximations," SIAM J. Control Optim., vol. 34, pp. 1291-1299, 1996.
16. J. P. Hespanha, "Stabilization through hybrid control," in Encyclopedia of Life Support Systems, 2005, to be published.
17. J. P. Hespanha, "Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle," IEEE Trans. Autom. Control, vol. 49, no. 3, pp. 470-482, Mar. 2004.
18. J. P. Hespanha, D. Liberzon, and E. D. Sontag, "Nonlinear observability and an invariance principle for switched systems," in Proc. 41st IEEE Conf. Decision and Control, 2002, pp. 4300-4305.
19. J. P. Hespanha and A. S. Morse, "Stability of switched systems with average dwell-time," in Proc. 38th IEEE Conf. Decision and Control 1999, pp. 2655-2660.
20. A. Isidori, Nonlinear Control Systems, 3rd ed. Berlin, Germany: Springer-Verlag, 1995.
21. C. M. Kellett, H. Shim, and A. R. Teel, "Further results on robustness of (possibly discontinuous) sample and hold feedback," IEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1081-1089, Jul. 2004.
22. H. K. Khalil, Nonlinear Systems, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1996.
23. M. Krichman, E. D. Sontag, and Y. Wang, "Input-output-to-state stability," SIAM J. Control Optim., vol. 39, pp. 1874-1928, 2001.
24. J. P. LaSalle, "Some extensions of Liapunov's second method," IRE Trans. Circuit Theory, vol. 7, pp. 520-527, 1960.
25. Z. G. Li, C. Y. Wen, and Y. C. Soh, "Switched controllers and their applications in bilinear systems," Automatica, vol. 37, pp. 477-481, 2001.
26. D. Liberzon, Switching in Systems and Control, Boston, MA: Birkhäuser, 2003.
27. D. Liberzon, A. S. Morse, and E. D. Sontag, "Output-input stability and minimum-phase nonlinear systems," IEEE Trans. Autom. Control, vol. 47, no. 3, pp. 422-436, Mar. 2002.
28. Y. Lin, E. D. Sontag, and Y. Wang, "A smooth converse Lyapunov theorem for robust stability," SIAM J. Control Optim., vol. 34, pp. 124-160, 1996.
29. F. M. Pait and A. S. Morse, "A cyclic switching strategy for parameter-adaptive control," IEEE Trans. Autom. Control, vol. 39, no. 6, pp. 1172-1183, Jun. 1994.
30. S. N. Singh, "Invertibility of observable multivariable nonlinear systems," IEEE Trans. Autom. Control, vol. AC-27, no. 2, pp. 487-489, Apr. 1982.
31. E. D. Sontag, "On the observability of polynomial systems, I: Finite-time problems," SIAM J. Control Optim., vol. 17, pp. 139-151, 1979.
32. E. D. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Autom. Control, vol. 34, no. 4, pp. 435-443, Apr. 1989.
33. E. D. Sontag, "A "universal" construction of Artstein's theorem on nonlinear stabilization," Syst. Control Lett., vol. 13, pp. 117-123, 1989.
34. E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed. New York: Springer-Verlag, 1998.
35. E. D. Sontag, "Stability and stabilization: Discontinuities and the effect of disturbances," in Nonlinear Analysis, Differential Equations and Control, F. H. Clarke, R. J. Stern, and G. Sabidussi, Eds. Dordrecht, The Netherlands: Kluwer, 1999, pp. 551-598.
36. E. D. Sontag and Y. Wang, "Output-to-state stability and detectability of nonlinear systems," Syst. Control Lett., vol. 29, pp. 279-290, 1997.
37. A. R. Teel and L. Praly, "Tools for semiglobal stabilization by partial state and output feedback," SIAM J. Control Optim., vol. 33, pp. 1443-1488, 1995.
38. J. Zhang, K. H. Johansson, J. Lygeros, S. S. Sastry, "Dynamical systems revisited: Hybrid systems with Zeno executions," in Proc. 3rd Int. Workshop on Hybrid Systems: Computation and Control, vol. 1790, N. Lynch and B. H. Krogh, Eds., 2000, pp. 451-464.
39. J. Zhao and D. J. Hill, "Passivity and stability of switched systems: A multiple storage function method," presented at the 3rd IEEE Conf. Decision and Control, 2004.