Lyapunov and Riccati equations of discrete-time descriptor systems

IEEE Transactions on Automatic Control

Volumn 44, Issue 11, 1999, Pages 2134-2139

  Zhang, Liqian ^a   Lam, James ^a   Zhang, Qingling ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; LYAPUNOV METHODS; OBSERVABILITY; RICCATI EQUATIONS; STATE FEEDBACK; SYSTEM STABILITY;

DISCRETE TIME DESCRIPTOR SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 0033322623     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.802931     Document Type: Article

References (21)

1. D. J. Bender, " Lyapunov-like equations and reachability/observability Grammians for descriptor systems," IEEE Trans. Automat. Contr., vol. AC-32, pp. 343-348, Apr. 1987.
2. D. Cobb. "Feedback and pole-placement in descriptors-variable systems," Int. J. Contr., vol. 33, pp. 1135-1146, 1981.
3. _, "Controllability, observability, and duality in singular systems," IEEE Trans. Automat. Contr., vol. AC-29, pp. 1076-1082, Dec. 1984.
4. L. Dai, Singular Control Systems. New York: Springer-Verlag, Lecture Notes in Contr. Inform. Sci., 1989.
5. R. E. Kalman and J. E. Bertram, "Control system analysis and design via the second method of Lyapunov - I: Continuous-time case," ASME J. Basic Eng., pp. 51-60, 1964.
6. V. Kucera, Analysis and Design of Discrete Linear Control Systems. Prentice-Hall International (UK) Ltd., Prentice-Hall Int. Ser. Syst. Contr. Eng., 1991.
7. F. L. Lewis, "Fundamental, reachability, and observability matrices for descriptor systems," IEEE Trans. Automat. Contr., vol. AC-30, pp. 502-505, May 1985.
8. _, "A survey of singlar systems," Circuits Syst. Signal Process., vol. 5, pp. 3-36, 1986.
9. F. L. Lewis and B. G. Mertzios, "On the analysis of discrete lineaar time-invariant singular systems," IEEE Trans. Automat. Contr., vol. 35, pp. 506-511, 1990.
10. D. G. Luenberger, "Dynamic equation in descriptor form," IEEE Trans. Automat. Contr., vol. AC-22, pp. 312-321, 1977.
11. _, "Time-invariant descriptor systems," Automatica, vol. 14, pp. 473-480, 1978.
12. B. G. Mertzios and F. L. Lewis, "Fundamental matrix of discrete singular systems," Circuits Syst. Signal Process., vol. 8, no. 3, pp. 341-354, 1989.
13. B. C. Moore, "Principal component analysis in linear systems: Controllability, observability, and model reduction," IEEE Trans. Automat. Contr., vol. AC-26, no. 1, pp. 17-32, 1981.
14. T. Pappas, A. J. Laub, and N. R. Sandel, "On the numberical solution of the discrete-time algebraic Riccati equation," IEEE Trans. Automat. Contr., vol. AC-25, no. 4, pp. 631-641, 1980.
15. V. L. Syrmos, P. Misra, and R. Aripirala, "On the discrete generalized Lyapunov equations," Automatica, vol. 31, no. 2, pp. 297-301, 1995.
16. K. Takaba, N. Morihira, and T. Katayama, "A generalized Lyapunov theorem for descriptor systems," Syst. Contr. Lett., vol. 24, pp. 49-51, 1995.
17. E. L. Yip and R. F. Sincovec, "Solvability, controllability and observability of continous descriptor systems," IEEE Trans. Automat. Contr., vol. AC-26, no. 3, pp. 702-706, 1981.
18. Q. L. Zhang, G. Z. Dai, and J. Lam, "Lyapunov equations and Riccati equations for descriptor systems," in Proc. 35th IEEE Conf. Decision Contr., 1996, pp. 4262-4263.
19. Q. L. Zhang and X. H. Xu, "Robust control for descriptor systems," in Proc. 33rd IEEE Conf. Decision Contr., 1994, pp. 2981-2982.
20. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
21. Z. Zhou, M. A. Sheyman, and T. Tarn, "Singular systems: A new approach in the time domain," IEEE Trans. Automat. Contr., vol. 32, pp. 42-50, 1987.