Sliding mode control synthesis of uncertain time-delay systems

Asian Journal of Control

Volumn 5, Issue 4, 2003, Pages 568-577

  Orlov, Yuri ^a   Perruquetti, Wilfrid ^b   Richard, Jean Pierre ^b  

^a CENTRO DE INVESTIGACIÓN CIENTÍFICA Y DE EDUCACIÓN SUPERIOR DE ENSENADA   (Mexico)

^b ECOLE CENTRALE DE LILLE   (France)

Author keywords

Robustness; Sliding mode; Time delay system

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP CONTROL SYSTEMS; DELAY CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); SLIDING MODE CONTROL; UNCERTAIN SYSTEMS;

DELAY OR DISTURBANCE DEPENDENT; STABILITY CRITERION; TIME DELAY SYSTEM;

CONTROL SYSTEM SYNTHESIS;

EID: 2942620215     PISSN: 15618625     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1934-6093.2003.tb00173.x     Document Type: Article

References (27)

1. Basin, M.V., L. Fridman, and M. Skliar, Optimal and Robust Integral Sliding Mode Filter Design for Systems with Continuous and Delayed Measurements, Proc. The 41st IEEE Conf. Decis. Contr., Las Vegas, USA, pp. 2594-2599 (2002).
2. Boyd, S., L. El Ghaoui, E. Feron, and V. Balakrishan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia (1994).
3. Byrnes, C.I., I.G. Lauko, D.S. Gilliam, and V.I. Shubov, Output Regulation for Linear Distributed Parameter Systems, IEEE Trans. Automat. Contr., Vol. 45, pp. 2236-2252 (2000).
4. Choi, H.H., An LMI Approach to Sliding Mode Control Design for a Class of Uncertain Time-Delay Systems, Proc. Eur. Contr. Conf., Karlsruhe, Germany (1999).
5. Conte, G. and A.-M. Perdon, Systems Over Rings: Theory and Applications, Plenary Lecture, Proc. IFAC Workshop Linear Time Delay Syst., Grenoble, France, p. 223-234 (1998).
6. Curtain, R.F. and H.J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Springer-Verlag, New York (1995).
7. El-Khazali, R., Variable Structure Robust Control of Uncertain Time-Delay Systems, Automatica, Vol. 34, No. 3, pp. 327-332 (1998).
8. Foias, C., H. Ozbay, and A. Tannenbaum, Robust Control of Infinite Dimensional Systems: Frequency Domain Methods, Springer-Verlag, London (1996).
9. Gouaisbaut, F., Y. Blanco, and J.P. Richard, Robust Sliding Mode Control of Nonlinear Systems with Delay: A Design via Polytropic Formulation, Int. J. Contr., (to be published) (2002).
10. Gouaisbaut, F., M. Dambrine, and J.R Richard, Robust Control of Delay Systems: A Sliding Mode Control Design via LMI, Syst. Contr. Lett., Vol. 46, No. 4, pp. 219-230 (2002).
11. ∞-Control for Distributed Parameter Systems: A State-Space Approach, Birkhauser, Boston (1993).
12. Krein, S.G., Linear Differential Equations in Banach Space. American Mathematical Society, Providence (1971).
13. Kolmanovskii, V.B. and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht (1999).
14. Levaggi, L., Sliding Modes in Banach Spaces, Differential Integral Equal., Vol. 15, pp. 167-189 (2002).
15. Levaggi, L., Infinite Dimensional Systems Sliding Motions, Eur. J. Contr., Vol. 8, pp. 508-517 (2002).
16. Li, X., and C.E. De Souza, Delay-Dependent Robust Stability and Stabilization of Uncertain Linear Delay System: A Linear Matrix Inequality Approach, IEEE Trans. Automat. Contr., Vol. 42, No 8, pp. 1144-1148 (1997).
17. Orlov, Y., Discontinuous Unit Feedback Control of Uncertain Infinitedimensional Systems, IEEE Trans. Automat. Contr., Vol. 45, pp. 834-843 (2000).
18. Orlov, Y., and D. Dochain, Discontinuous Feedback Stabilization of Minimum-Phase Semilinear Infinite-Dimensional Systems with Application to Chemical Tubular Reactor, IEEE Trans. Automat. Contr., Vol. 47, pp. 1293-1304 (2002).
19. Orlov, Y. and V.I. Utkin, Sliding Mode Control in Infinite-Dimensional Systems, Automatica, Vol. 23, pp.753-757 (1987).
20. Shyu, K.K. and J.J. Yan, Robust Stability of Uncertain Time-Delay Systems and Its Stabilization by Variable Structure Control, Int. J. Contr., Vol. 57, No. 1, pp. 237-246 (1993).
21. Su, J.H., Further Results on the Robust Stability of Delay Dependence for Linear Uncertain Systems, Syst. Contr. Lett., Vol. 23, pp. 375-379 (1994).
22. Su, J.H. and C.G. Huang, Robust Stability on Delay Dependence for Linear Uncertain Systems, IEEE Trans. Autamat. Contr., Vol. 37, pp. 1656-1659 (1992).
23. Utkin, V.I., Sliding Modes in Control Optimization. Springer-Verlag, Berlin (1992).
24. Utkin, V.I., J. Guldner, and J. Shi, Sliding Modes in Electromechanical Systems, Taylor and Francis, London (1999).
25. Zheng, F. and P. M. Frank, Finite Dimensional Variable Structure Control Design for Distributed Delay Systems, Int. J. Contr., Vol. 74, No. 4, pp. 398-408 (2001).
26. Xie, L. and C.E. De Souza C.E, Robust Stabilization and Disturbance Attenuation for Uncertain Delay Systems, Proc. Eur. Contr. Conf., Groningen, The Netherlands (1993).
27. Zolezzi, T., Variable Structure Control of Semilinear Evolution Equations, Partial Differential Equations and the Calculus of Variations, Essays in honor of Ennio De Giorgi, Birkhauser, Boston, Vol. 2, pp. 997-1018 (1989).