The regulator problem for linear systems with saturations on the control and its increments or rate: An LMI approach

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 53, Issue 12, 2006, Pages 2681-2691

  Benzaouia, Abdellah ^a   Tadeo, Fernando ^b   Mesquine, Fouad ^a  

^a CADI AYYAD UNIVERSITY   (Morocco)

^b UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Asymmetric constraints; Control increment or rate; Control saturation; Linear matrix inequality (LMI) technique; Linear systems; Reduced order system

Indexed keywords

CONSTRAINT THEORY; CONTROL SYSTEM ANALYSIS; PROBLEM SOLVING; STATE SPACE METHODS;

ASYMMETRIC CONSTRAINTS; CONTROL INCREMENT; CONTROL RATE; CONTROL SATURATION; LINEAR MATRIX INEQUALITY; REDUCED-ORDER SYSTEM;

LINEAR CONTROL SYSTEMS;

EID: 33845901011     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2006.883163     Document Type: Article

References (25)

1. D. Angeli, A. Casavola, and E. Mosca, "Predictive PI-control of linear plants under positional and incremental input saturations," Automatica, vol. 36, no. 10, pp. 1505-1516, 2000.
2. A. Bateman and Z. Lin, "An analysis and design method for linear systems under nested saturation," Syst. Contr. Lett., vol. 48, pp. 41-52, 2003.
3. A. Benzaouia and C. Burgat, "Regulator problem for linear discrete-time systems with nonsymmetrical constrained control," Int. J. Contr., vol. 48, no. 6, pp. 2441-2451, 1988.
4. A. Benzaouia, "The resolution of equation XA + XBX = HX and the pole assignment problem," IEEE Trans. Autom. Contr., vol. 39, no. 10, pp. 2091-2095, Oct. 1994.
5. A. Benzaouia and A. Baddou, "Piecwise linear constrained control for continuous time systems," IEEE Trans. Autom. Contr., vol. 44, no. 7, p. 1477, Jul. 1999.
6. A. Benzaouia and S. El Faiz, "The regulator problem for linear systems with constrained control: An LMI approach," IMA J. Math. Contr. Inf., to be published.
7. A. Benzaouia, M. A. Rami, and S. El Faiz, "Stabilization of linear systems with saturation: A Sylvester equation approach," IMA J. Math. Comr. Inf., vol. 21, no. 3, pp. 247-259, 2004.
8. F. Blanchini, "Set invariance in control," Automatica, vol. 35, pp. 1747-1767, 1999.
9. J. M. Berg, K. D. Hammett, C. A. Schwartz, and S. S. Banda, "An analysis of the destabilizing effect of daisy chained rate limited actuators," IEEE Trans. Contr. Syst. Technol., vol. 4, no. 1, pp. 171-176, Jan. 1996.
10. S. Boyd, L. EL Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
11. J. J. Dongarra, S. Hammarling, and J. Wilkinson, "Numerical considerations in computing invariant subspaces," SIAM J. Matrix Anal. Appl., vol. 13, no. 1, pp. 145-161, 1992.
12. M. A. Dornheim, "Report pinpoints factors leading to YF-22 crash," Aviation Week Space Technol., vol. 9, pp. 53-54, 1992.
13. G. Feng, M. Palaniswami, and Y. Zhu, "Stability of rate constrained robust pole placement adaptive control systems," Syst. Contr. Lett., vol. 18, pp. 99-107, 1992.
14. E. G. Gilbert and K. T. Tan, "Linear systems with state and control constraints: The theory and application of maximal output admissible sets," IEEE Trans. Autom. Contr., vol. 36, no. 11, pp. 1008-1020, Nov. 1991.
15. T. Hu and Z. Lin, "The equivalence of several set invariance conditions under saturations," in Proc. 41st IEEE Conf. Decision and Control, Las Vegas, NM, 2002.
16. T. Hu, Z. Lin, and B. M. Chen, "Analysis and design for discrete-time linear systems subject to actuator saturation," Syst. Contr. Lett., vol. 45, pp. 97-112, 2002.
17. T. Hu, Z. Lin, and B. M. Chen, "An analysis and design method for linear systems subject to actuator saturation and disturbance," Automatica, vol. 3 8, pp. 351-359, 2002.
18. P. Kapasouris and M. Athans, "Control systems with rate and magnitude saturation for neutrally stable open-loop systems," in Proc. IEEE Conf. Decision and Control, Honolulu, HI, 1990, pp. 3404-3409.
19. Z. Lin, "Senti-global stabilization of linear systems with position and rate-limited actuators," Syst. Contr. Lett., vol. 30, pp. 1-11, 1997.
20. Z. Lin, M. Pachter, S. Banda, and Y. Shamash, "Stabilizing feedback design for linear systems with rate limited actuators," in Control of Uncertain Systems with Bounded Inputs. New York: Springer Verlag, 1997, vol. 227, pp. 173-186.
21. Z. Lin, A. Saberi, and A. A. Stoorvogel, "Semi-global stabilization of linear discrete-time systems subject to input saturation via linear feedback. An ARE-based approach," in Proc. 33rd CDC, Lake Buena Vista, FL, Dec. 1994.
22. F. Mesquine, F. Tadeo, and A. Benzaouia, "Regulator problem for linear systems with constraints on the control and its increments or rate," Automatica, vol. 40, no. 8, pp. 1378-1395, 2004.
23. F. Mesquine, F. Tadeo, and A. Benzaouia, "Regulator constrained control and rate problem for linear systems with additive disturbances," in Proc. Amer. Conf. Contr. (ACC), Boston, Ma, Jun.-Jul. 30-2, 2004.
24. L. Trygve, R. Murray, and T. Y. Fossen, "Stabilization of integrator chains in the presence of magnitude and rate saturations; A gain scheduling approach," in Proc. IEEE Conf. Decision and Control, San Diego, CA, 1997, pp. 4004-4005.
25. F. Tyan and D. S. Bernstein, "Dynamic output feedback compensation for linear systems with independent amplitude and rate saturations," Int. J. Contr., vol. 67, no. 1, pp. 89-116, 1997.