Controllability and observability for a class of controlled switching impulsive systems

IEEE Transactions on Automatic Control

Volumn 53, Issue 10, 2008, Pages 2360-2366

  Liu, Bin ^a,b   Marquez, Horacio J ^c  

^a HUNAN UNIVERSITY OF TECHNOLOGY   (China)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Controllability; Controlled observability; Hybrid systems; Switching impulsive systems; Variation of parameters

Indexed keywords

COLLISION AVOIDANCE; CONTROLLABILITY; LINEAR SYSTEMS; OBSERVABILITY; SWITCHING; TIME SHARING SYSTEMS; TIME VARYING CONTROL SYSTEMS; TIME VARYING SYSTEMS;

CHARACTERISTIC POLYNOMIALS; CONTROLLED OBSERVABILITY; CONTROLLED SWITCHING; HYBRID SYSTEMS; IMPULSIVE SYSTEMS; LINEAR IMPULSIVE; NECESSARY AND SUFFICIENT CONDITIONS; SWITCHING TIMES; VARIATION OF PARAMETERS;

CONTROL THEORY;

EID: 56549106713     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.2007476     Document Type: Article

References (31)

1. A. Levis, S. Marcus, W. Perkins, P. Koktovic, M. Athans, R. Brockett, and A. Willsky, "Challenge to control, A collective view," IEEE Trans. Automat. Control, vol. AC-32, no. 12, pp. 274-285, Dec. 1987.
2. M. S. Branicky, V. S. Borkar, and S. K. Mitter, "A unified framework for hybrid control: Model and optimal control theory," IEEE Trans. Automat. Control, vol. AC-43, no. 1, pp. 31-45, Jan. 1988.
3. A. N. Michel, "Recent trends in the stability analysis of hybrid dynamical systems," IEEE Trans. Automat. Control, vol. 45, no. 1, pp. 120-134, Jan. 1999.
4. S. H. Lee and J. T. Lim, "Stability analysis of switched systems with impulse effects," in Proc. IEEE Conf. Intel. Contr./Antel. Syst., Cambridge, MA, 1999, pp. 15-17.
5. V. Lakshimikantham and X. Z. Liu, "Impulsive hybrid systems and stability theory," Dyn. Syst. Appl., vol. 7, pp. 1-9, 1998.
6. M. S. 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.
7. B. Liu, X. Z. Liu, and X. X. Liao, "Stability and robust stability of quasi-linear impulsive hybrid dynamical systems," J. Math. Anal. Appl., vol. 283, pp. 416-430, 2003.
8. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulse Differential Equations. Singapore: Singapore World Scientific, 1989.
9. J. P. Aubin, J. Lygeros, M. Quinncampoix, S. Sastry, and N. Seube, "Impulse differential inclusions: A viability approach to hybrid systems," IEEE Trans. Automat. Control, vol. 47, no. 1, pp. 1-20, Jan. 2002.
10. J. Lygeros, K. H. Johansson, S. N. Simić, J. Zhang, and S. Sastry, "Dynamical properties of hybrid automata," IEEE Trans. Automat. Control, vol. 48, no. 2, pp. 2-17, Feb. 2003.
11. J. Ezzine and A. H. Haddad, "Controllability and observability of hybrid systems," Int. J. Control, vol. 49, pp. 2045-2055, 1989.
12. X. Z. Liu, "Impulsive control and optimization," Appl. Math. Computat., vol. 73, pp. 77-98, 1995.
13. X. Z. Liu and A. R. Willms, "Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft," Math. Problems Eng., vol. 2, pp. 277-299, 1996.
14. S. Leela, F. A. McRae, and S. Sivasundaram, "Controllability of impulsive differential equations," J. Math. Anal. Appl., vol. 177, no. 1, pp. 24-30, 1993.
15. R. K. George, A. K. Nandakumaran, and A. Arapostathis, "A note on controllability of impulsive systems," J. Math. Anal. Appl., vol. 241, pp. 276-283, 2000.
16. Z. Benzaid and M. Sznaier, "Constrained controllability of linear impulsive differential systems," IEEE Trans. Automat. Control, vol. 39, no. 5, pp. 1064-1066, May 1994.
17. C. J. Wang, "Controllability and observability of linear time-varying singular systems," IEEE Trans. Automat. Control, vol. 44, no. 10, pp. 1901-1905, Oct. 1999.
18. G. M. Xie and L. Wang, "Controllability and stabilizability of switched linear-systems," Syst. Control Lett., vol. 48, no. 2, pp. 135-155, 2003.
19. C. T. Chen, Linear Systems Theory and Design. New York: Holt, Rinehart and Winston, 1984.
20. G. Stikkel, J. Bokor, and Z. Szabó, "Necessary and sufficient condition for the controllability of switching linear hybrid systems," Automatica, vol. 40, pp. 1093-1097, 2004.
21. Z. G. Li, C. B. Soh, and X. H. Xu, "Controllability and observability of impulsive hybrid dynamic systems," IMA J. Math. Control Inform. vol. 16, pp. 315-334, 1999.
22. Z. G. Li, Y. C. Soh, and C. Y. Wen, "Robust stability of a class of hybrid nonlinear systems," IEEE Trans. Automat. Control, vol. 46, no. 6, pp. 897-903, Jun. 2001.
23. Z. G. Li, Y. C. Soh, and C. Y. Wen, Switched and Impulsive Systems: Analysis, Design and Application. New York: Springer-Verlag, 2005.
24. Z. G. Li, C. Y. Wen, and Y. C. Soh, "Analysis and design of impulsive control systems," IEEE Trans. Automat. Control, vol. 46, no. 6, pp. 894-899, Jun. 2001.
25. B. Liu, X. Liu, G. Chen, and H. Wang, "Robust impulsive synchronization of uncertain dynamical networks," IEEE Trans. Circuits Syst. I: Regular Paper, vol. 52, no. 7, pp. 1431-1441, Jul. 2005.
26. T. Yang, Impulsive Control Theory. Berlin, Germany: Springer Verlag, 2001.
27. D. Liberzon, Switching in Systems and Control. Boston, MA: Birkhäuser, 2003.
28. Z. H. Guan, D. J. Hill, and X. Shen, "On hybrid impulsive and switching systems and applications on nonlinear control," IEEE Trans. Automat. Control, vol. 50, no. 7, pp. 1058-1062, Jul. 2005.
29. Z. G. Li, C. Y. Wen, and Y. C. Soh, "Observer-based stabilization of switching linear system," Automatica, vol. 39, pp. 517-523, 2003.
30. D. Z. Cheng, "Controllability of switched bilinear-systems," IEEE Trans. Automat. Control, vol. 50, no. 4, pp. 511-515, Apr. 2005.
31. Z. Sun, S. S. Ge, and T. H. Lee, "Controllability and reachability criteria for switched linear systems," Automatica, vol. 38, no. 5, pp. 775-786, 2002.