Saturated feedback stabilization of discrete-time descriptor bilinear systems

IEEE Transactions on Automatic Control

Volumn 52, Issue 9, 2007, Pages 1700-1704

  Lu, Guoping ^a   Feng, Gang ^b   Jiang, Zhong Ping ^c  

^a NANTONG UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Discrete time bilinear descriptor systems; Global asymptotic stabilization; Saturated controller; State feedback

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP CONTROL SYSTEMS; FEEDBACK CONTROL; INVARIANCE; LINEAR SYSTEMS; NUMERICAL METHODS;

BILINEAR SYSTEMS; DISCRETE-TIME DESCRIPTOR; IMPLICIT FUNCTION THEOREM;

DISCRETE TIME CONTROL SYSTEMS;

EID: 34648828784     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.904282     Document Type: Article

References (28)

1. p stabilization of discrete-time linear systems subject to actuator saturation: The case of p = 1," IEEE Trans. Autom. Control, vol. 48, no. 12, pp. 2196-2198, 2003.
2. L. Dai, Singular Control Systems. Berlin, Germany: Springer-Verlag, 1989.
3. ∞ control for descriptor systems with non-linear uncertainties," Int. J. Contr., vol. 76, no. 12, pp. 1254-1262, 2003.
4. J. P. LaSalle, The Stability and Control of Discrete Process. New York: Springer-Verlag, 1986.
5. F. L. Lewis, B. G. Mertzios, and W. Marszalek, "Analysis of singular bilinear systems using Walsh functions," Proc. Inst. Elect. Eng. Contr. Theory Applicat., vol. 138, no. 2, pp. 89-92, 1991.
6. J. L. Lin and S. J. Chen, "Robust analysis of uncertain linear singular systems with output feedback control," IEEE Trans. Autom. Control vol. 44, no. 10, pp. 1924-1929, 1999.
7. C. Lin, J. Lam, J. L. Wang, and G. H. Yang, "Analysis on robust stability for interval descriptor systems," Syst. Contr. Lett., vol. 42, no. 4, pp. 267-278, 2001.
8. T. Hu, Z. Lin, and B. M. Chen, "Analysis and design for linear discrete-time systems subject to actuator saturation," Syst. Contr. Lett., vol. 45, no. 2, pp. 97-112, 2002.
9. T. Hu and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design. Boston, MA: Birkhäuser, 2001.
10. G. P. Lu and D. W. C. Ho, "Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation," IEEE Trans. Autom. Control, vol. 51, no. 5, 2006.
11. G. P. Lu and D. W. C. Ho, "Continuous stabilization controllers for singular bilinear systems: The state feedback case," Automatica, vol. 42, no. 2, pp. 309-314, 2006.
12. D. W. C. Ho and G. P. Lu, "Robust stabilization for a class of discrete-time nonlinear systems via output feedback: The unified LMI approach," Int. J. Contr., vol. 76, pp. 105-115, 2003.
13. G. P. Lu, Y. F. Zheng, and C. S. Zhang, "Dynamical output feedback stabilization of MIMO bilinear systems with undamped natural response," Asian J. Contr., vol. 5, no. 2, pp. 251-260, 2003.
14. ∞ control for descriptor systems: A matrix inequalities approach," Automatica vol. 33, pp. 669-673, 1997.
15. R. R. Mohler, Nonlinear Systems: V.2 Application to Bilinear Control Englewood Cliffs, NJ: Prentice-Hall, 1991.
16. C. D. Rahn, "Stabilizability conditions for strictly bilinear systems with purely imaginary spectra," IEEE Trans. Autom. Control, vol. 41, pp. 1346-1347, 1996.
17. D. N. Shields, "Observer design for discrete nonlinear descriptor systems," in Proc. Int. Conf. Contr., Sept. 1996, vol. 2, pp. 831-836.
18. ∞ control for non-linear descriptor systems," IEEE Trans. Autom. Control, vol. 47, pp. 1919-1925, 2002.
19. Z. D. Wang, D. P. Goodall, and K. J. Burnham, "On designing observers for time-delay systems with nonlinear disturbances," Int. J. Contr. vol. 75, no. 11, pp. 803-811, 2002.
20. H. S. Wu and K. Mizukami, "Stability and robust stabilization of non-linear descriptor systems with uncertainties," in Proc. 33rd IEEE Conf. Decision Contr., 1994, vol. 3, pp. 2772-2777.
21. S. Y. Xu, P. V. Dooren, R. Stefan, and J. Lam, "Robust stability and stabilization for singular systems with state delay and parameter uncertainty," IEEE Trans. Autom. Control, vol. 47, pp. 1122-1128, 2002.
22. S. Y. Xu, J. Lam, and C. W. Yang, "Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay," Syst. Contr. Lett., vol. 43, no. 2, pp. 77-84, 2001.
23. S. Y. Xu and J. Lam, "Robust stability and stabilization of discrete singular systems: An equivalent characterization," IEEE Trans. Autom. Control, vol. 49, no. 4, pp. 568-574, 2004.
24. M. Zasadzinski, H. S. Ali, H. Rafaralahy, and E. Magarotto, "Disturbance decoupled diagnostic observer for singular bilinear systems," in Proc. Amer. Contr. Conf., 2001, vol. 2, pp. 1455-1460.
25. M. Zasadzinski, E. Magarotto, H. Rafaralahy, and H. S. Ali, "Residual generator design for singular bilinear systems subjected to unmeasurable disturbances: An LMI approach," Automatica, vol. 39, pp. 703-713, 2003.
26. H. S. Zhang, L. H. Xie, and Y. C. Soh, "Optimal recursive state estimation for singular stochastic discrete-time systems," in Proc. 37th IEEE Conf. Decision Contr., 1998, vol. 3, pp. 2908-2913.
27. H. S. Zhang, L. H. Xie, and Y. C. Soh, "Optimal recursive filtering, prediction, and smoothing for singular stochastic discrete-time systems," IEEE Trans. Autom. Control, vol. 44, no. 11, pp. 2154-2158, 1999.
28. H. S. Zhang, L. H. Xie, Y. C. Soh, and W. Wang, "Steady state risk-sensitive estimation for discrete-time singular systems," in Proc. Int. Conf. Contr. Automat., Jun. 16-19, 2002, p. 125.