Quadratic stabilization of switched systems

International Journal of Systems Science

Volumn 36, Issue 7, 2005, Pages 395-404

  Ji, Zhijian ^a,b   Wang, Long ^a,c,d,e   Xie, Guangming ^a  

^a PEKING UNIVERSITY   (China)

^b QINGDAO UNIVERSITY   (China)

^c Department of Dynamics and Control ^*  (China)

^d National Key Laboratory of Complex Systems and Turbulence   (China)

^e NATIONAL NATURAL SCIENCE FOUNDATION OF CHINA   (China)

Author keywords

Feedback stabilization; Lyapunov method; Quadratic stability; Switching rule; Uncertain switched systems

Indexed keywords

FEEDBACK STABILIZATION; QUADRATIC STABILILITY; SWITCHING RULES; UNCERTAIN SWITCHED SYSTEMS;

CONTROL EQUIPMENT; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK; LYAPUNOV METHODS; TIME VARYING SYSTEMS; UNCERTAIN SYSTEMS;

SWITCHING SYSTEMS;

EID: 27944493911     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720500140003     Document Type: Article

References (23)

1. V. Blondel and J. Tsitsiklis, "NP-hardness of some linear control design problems", SIAM J. Control Optim., 35, pp. 2118-2127, 1997.
2. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control theory, Philadelphia, PA: SIAM, 1994.
3. D. Cheng, "Stabilization of planar switched systems", Syst. Control. Lett., 51, pp. 79-88, 2004.
4. E. Feron, "Quadratic stabilizability of switched system via state and output feedback", MIT Technical Report CICS-P-468 (1996).
5. ∞ control theory", IEEE Trans. Autom. Control, 35, pp. 356-361, 2001.
6. D. Liberzon and A.S. Morse, "Basic problems in stability and design of switched systems", IEEE Control Syst. Mag., 19, pp. 59-70, 1999.
7. J. Malmborg, B. Bernhardsson and K.J. Astrom, "A stabilizing switching scheme for multi controller systems", in Proceedings of the 13th IFAC World Congress, San Francisco, CA, 1996, pp. 229-234.
8. P. Peleties and R.A. DeCarlo, "Asymptotic stability of m-switched systems using Lyapunov-like functions", in Proceedings of the American Control Conference, Boston, MA, 1991, pp. 1679-1684.
9. I.R. Petersen, "A stabilization algorithm for a class of uncertain linear systems", Sys. Control Lett., 8, pp. 351-357, 1987.
10. S. Pettersson, "Synthesis of switched linear systems", in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, 2003, pp. 5283-5288.
11. S. Pettersson and B. Lennartson, "Stabilization of hybrid systems using a min-projection strategy", in Proceedings of the American Control Conference, 2001, pp. 223-228.
12. M.A. Rotea and P.P. Khargonekar, "Stabilization of uncertain systems with norm bounded uncertainty - a control lyapunov function approach", SIAM J. Control Optim., 27, pp. 1462-1476, 1989.
13. E. Skalidas, R.J. Evans, A.V. Savkin and I.R. Petersen, "Stability results for switched controller systems", Automation, 35, pp. 553-564, 1999.
14. Z. Sun, S.S. Ge and T.H. Lee, "Controllability and reachability criteria for switched linear systems", Automationca, 38, pp. 775-786, 2002.
15. M.A. Wicks and R.A. DeCarlo, "Solution of coupled Lyapunov equations for the stabilization of multi-modal linear systems", in Proceedings of the American Control Conference, 1997, pp. 1709-1713.
16. MA. Wicks, P. Peleties and R.A. DeCarlo, "Construction of piecewise Lyapunov functions for stabilizing switched systems", in Proceedings of the 33rd IEEE Conference on Decision and Control, Orlando, FL, December 1994, pp. 3492-3497.
17. G. Xie and L. Wang, Quadratic stabilizability of switched linear systems. Technical Report, Center for Systems and Control, Peking University (2002).
18. G. Xie and L. Wang, "Controllability and stabilizability of switched linear systems", Syst. Control Lett., 48, pp. 135-155, 2003.
19. G. Xie, D. Zheng and L. Wang, "Controllability of switched linear systems", IEEE Trans. Autom. Control, 47, pp. 1401-1405, 2002.
20. X. Xu and P.J. Antsaklis, "Stabilization of second-order LTI switched systems", Int. J. Control, 73, pp. 1261-1279, 2000.
21. G. Zhai, "Quadratic stabilizability of discrete-time switched systems via state and output feedback", in Proceedings of the 40th Conference on Decision and Control, Orlando, FL, December 2001, pp. 2165-2166.
22. G. Zhai, H. Lin and P.J. Antsaklis, "Quadratic stabilizability of witched liner systems with polytopic uncertainties", Int. J. Control, 76, pp. 747-753, 2003.
23. J. Zhao and G.M. Dimirovski, "Quadratic stability of a class of switched non-linear systems", IEEE Trans. Autom. Control, 49, pp. 574-578, 2004.