Synthesis of controllers for continuous-time delay systems with saturating controls via LMI's

IEEE Transactions on Automatic Control

Volumn 45, Issue 1, 2000, Pages 105-111

  Tarbouriech, Sophie ^a   Gomes Da Silva Jr , João Manoel ^b  

^a LAAS CNRS   (France)

^b FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP CONTROL SYSTEMS; DELAY CONTROL SYSTEMS; FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; STATE FEEDBACK; SYSTEM STABILITY;

CONTINUOUS TIME DELAY SYSTEMS; CONTROL SATURATION; LINEAR MATRIX INEQUALITY; LOCAL STABILITY;

CONTROL SYSTEM SYNTHESIS;

EID: 0033903869     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.827364     Document Type: Article

References (26)

1. J. Alvarez-Ramirez, R. Suarez, and J. Alvarez, "Semiglobal stabilization of multi-input linear system with saturated linear state feedback," Syst. Contr. Lett., vol. 23, pp. 247-254, 1994.
2. D. S. Bernstein and A. N. Michel, "A chronological bibliography on saturating actuators," Int. J. Robust Nonlinear Contr., vol. 5, pp. 375-380, 1995.
3. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," in SIAM Studies Appl. Math. Philadelphia, PA, 1994.
4. B. S. Chen, S. S. Wang, and H. C. Lu, "Stabilization of time-delay systems containing saturating actuators," Int. J. Contr., vol. 47, pp. 867-881, 1988.
5. J. M. Gomes da Silva Jr., A. Fischman, S. Tarbouriech, J. M. Dion, and L. Dugard, "Synthesis of state feedback for linear systems subject to control saturation by an LMI-based approach," in Proc. ROCOND, Budapest, Hungary, June 1997, pp. 219-234.
6. J. K. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
7. J. C. Hennet and S. Tarbouriech, "Stability and stabilization of delay differential systems," Automatica, vol. 33, pp. 347-354, 1997.
8. M. Klaï, S. Tarbouriech, and C. Burgat, "Some independent-time-delay stabilization of linear systems with saturating controls," in Proc. IEE Contr.'94, Coventry, U.K., Mar. 1994, pp. 1358-1363.
9. N. N. Krasovskii, Stability of Motion. Stanford, CA: Stanford Univ. Press, 1963.
10. V. B. Kolmanovskii and V. R. Nosov, Stability of Functional Differential Equations. New York: Academic, 1986.
11. J. F. Lafay and G. Conte, "Analysis and design methods for delay systems," in Proc. 34th IEEE-CDC, New Orleans, Dec. 1995, pp. 2035-2069.
12. M. S. Mahmoud and N. F. Al-Muthairi, "Quadratic stabilizati on of continuous-time systems with state-delay and norm-bounded time-varying uncertainties," IEEE Trans. Automat. Contr., vol. 39, pp. 2135-2139, Oct. 1994.
13. A. P. Molchanov and E. S. Pyatnitskii, "Criteria of asymptotic stability of differential and difference inclusions encountered in control theory," Syst. Contr. Lett., vol. 13, pp. 59-64, 1989.
14. T. Mori, N. Fukuma, and M. Kuwahara, "On an estimate of the decay rate for stable linear delay systems," Int. J. Contr., vol. 36, pp. 95-97, 1982.
15. ∞ memory less control with an α-stability constraint for time-delays systems: An LMI approach," in Proc. 34th IEEE-CDC, New Orleans, Dec. 1995, pp. 1507-1512.
16. S.-I. Niculescu, J.-M. Dion, and L. Dugard, "Robust stabilization for uncertaintime-delay systems containing saturating actuators," IEEE Trans. Automat. Contr., vol. 41, pp. 742-747, May 1996.
17. I. R. Petersen, "Stabilization algorithm for a class of uncertain linear systems," Syst. Contr. Lett., vol. 8, pp. 181-188, 1987.
18. A. Saberi, Z. Lin, and A. R. Teel, "Control of linear systems with saturating actuators," IEEE Trans. Automat. Contr., vol. 41, pp. 368-378, Mar. 1996.
19. T. J. Su, P. L. Liu, and J. T. Tsay, "Stabilization of delay-dependence for saturating actuator systems," in Proc. 30th IEEE-CDC, Brighton, U.K., Dec. 1991, pp. 2891-2892.
20. H. J. Sussmann, E. D. Sontag, and Y. Yang, "A general result on the stabilization of linear systems using bounded controls," IEEE Trans. Automat. Contr., vol. 39, pp. ?-?, 1994.
21. S. Tarbouriech, "Local stabilization of continuous-time systems with bounded inputs," in Stability and Control of Time-Delay Systems. New York: Springer-Verlag, 1997, ch. 14.
22. S. Tarbouriech and G. Garcia, Control of Uncertain Systems with Bounded Inputs, S. Tarbouriech and G. Garcia, Eds. New York: Springer-Verlag, 1997.
23. _, "Robust stability of uncertain linear delay systems with saturating inputs: An LMI's approach," in Proc. IFAC Conf. Syst. Structure Contr., Nantes, France, July 1998, pp. 379-384.
24. A. Towsen, "Stable sampled-data feedback control of dynamic systems with time-delays," Int. J. Systems Sci., vol. 13, no. 12, pp. 1379-1384, 1982.
25. E. Tissir and A. Hmamed, "Further results on the stabilization of time delay systems containing sturating actuators," Int. J. Systems Sci., vol. 23, pp. 615-622, 1992.
26. G. F. Wredenhagen and P. R. Blanger, "Piecewise-linear LQ control for systems with inputs constraints," Automatica, vol. 30, pp. 403-416, 1994.