Stability analysis and design for switched descriptor systems

International Journal of Control, Automation and Systems

Volumn 7, Issue 3, 2009, Pages 349-355

  Zhai, Guisheng ^a   Kou, Ryuuen ^a   Imae, Joe ^a   Kobayashi, Tomoaki ^a  

^a Osaka Prefecture University   (Japan)

Author keywords

Arbitrary switching; Commutation; Convex combination; Descriptor systems; Stability analysis; Stabilization; Switched systems

Indexed keywords

ARBITRARY SWITCHING; COMMUTATION; CONVEX COMBINATION; DESCRIPTOR SYSTEMS; STABILITY ANALYSIS; SWITCHED SYSTEMS;

DESCRIBING FUNCTIONS; FARM BUILDINGS; LINEAR SYSTEMS; MATRIX ALGEBRA; STABILIZATION; SWITCHING; SWITCHING SYSTEMS;

SYSTEM STABILITY;

EID: 67949091303     PISSN: 15986446     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12555-009-0303-8     Document Type: Article

References (18)

1. K. S. Narendra and J. Balakrishnan, "A common Lyapunov function for stable LTI systems with commuting A-matrices," IEEE Trans. on Automatic Control, vol. 39, pp. 2469-2471, 1994.
2. F. L. Lewis, "A survey of linear singular systems," Circuits Systems Signal Process, vol. 5, pp. 3-36, 1986.
3. K. Takaba, N. Morihira, and T. Katayama, "A generalized Lyapunov theorem for descriptor systems," Systems & Control Letters, vol. 24, pp. 49-51, 1995.
4. S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SLAM, Philadelphia, 1994.
5. ∞ control for descriptor systems: a matrix inequalities approach," Automatica, vol. 33, pp. 669-673, 1997.
6. ∞ control of descriptor systems," Proc. of the 38th IEEE Conference on Decision and Control, Phoenix, USA, pp. 4092-4097, 1999.
7. D. Liberzon and A. S. Morse, "Basic problems in stability and design of switched systems," IEEE Control Systems Magazine, vol. 19, pp. 59-70, 1999.
8. R. DeCarlo, M. S. Branicky, S. Pertersson, and B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems," Proceedings of the IEEE, vol. 88, pp. 1069-1082, 2000.
9. Z. Sun and S. S. Ge, "Analysis and synthesis of switched linear control systems," Automatica, vol. 41, pp. 181-195, 2005.
10. D. Liberzon, J. P. Hespanha, and A. S. Morse, "Stability of switched systems: a Lie-algebraic condition," Systems & Control Letters, vol. 37, pp. 117-122, 1999.
11. M. A. Wicks, P. Peleties, and R. A. DeCarlo, "Construction of piecewise Lyapunov functions for stabilizing switched systems," Proc. of the 33rd IEEE Conference on Decision and Control, Orlando, USA, pp. 3492-3497, 1994.
12. S. Pertersson and B. Lennartson, "LMI for stability and robustness of hybrid systems," Proc. of the American Control Conference, Albuquerque, USA, pp. 1714-1718, 1997.
13. M. A. Wicks, P. Peleties, and R. A. DeCarlo, "Switched controller design for the quadratic stabilization of a pair of unstable linear systems," European Journal of Control, vol. 4, pp. 140-147, 1998.
14. F. R. Gantmacher, The Theory of Matrices, vol. II, pp. 24-49, Chelsea, 1959.
15. E. Feron, "Quadratic stabilizability of switched system via state and output feedback," MIT Technical Report CICS-P-468, 1996.
16. G. Zhai and K. Yasuda, "Stability analysis for a class of switched systems," Trans. of the Society of Instrument and Control Engineers, vol. 36, pp. 409-415, 2000.
17. K. C. Goh, M. G. Safonov, and G. P. Papavassilopoulos, "A global optimization approach for the BMI problem," Proc. of the 33rd IEEE Conference on Decision and Control, Orlando, USA, pp. 2009-2014, 1994.
18. ∞ controller design: a matrix inequality approach using a homotopy method," Automatica, vol. 37, pp. 565-572, 2001.