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Keywords:
relay-delay system; sliding mode controllers; input delay; state delay
Summary:
This paper provides an overview of recent results for relay-delay systems. In a first section, simple examples illustrate the problems induced by delays in the synthesis of sliding mode controllers. Then, a brief overview of the existing results shows the present advances and limits in this domain. The last parts of the paper are devoted to new results: first, for systems with state delay, then for systems with input delay.
References:
[1] Aggoune W.: Contribution à la Stabilisation de Systèmes Non Linéaires: Application Aux Systèmes Non Réguliers et Aux Systèmes à Retards. (In French.) INRIA Lorraine/CRAN, University of Metz 1999
[2] Bonnet C., Partington, J., Sorine M.: Robust control and tracking in $l_{\infty }$ of delay systems equipped with a relay sensor. In: LSS’98, 8th IFAC Conference Large Scale Systems, Patras 1998
[3] Cheres E., Gutman, S., Palmor Z.: Stabilization of uncertain dynamic systems including state delay. IEEE Trans. Automat. Control 34 (1989), 11, 1199–1203 DOI 10.1109/9.40753 | MR 1020938 | Zbl 0693.93059
[4] Choi H.: An LMI approach to sliding mode control design for a class of uncertain time delay systems. In: European Control Conference ECC’99, Karlsruhe 1999
[5] Choi S., Hedrick J.: An observer-based controller design method for improving air/fuel characterization of spark ignition engines. IEEE Trans. Control Syst. Technology 6 (1998), 3, 325–334 DOI 10.1109/87.668034
[6] Dambrine M., Gouaisbaut F., Perruquetti, W., Richard J.-P.: Robustness of sliding mode control under delays effects: a case study. In: Proc. 2nd IEEE-IMACS CESA’98, Comput. Eng. in Systems Applications, Hamamet 1998, pp. 817–821
[7] Carlo R. De, Zak, S., Matthews G.: Variable structure control of nonlinear variable systems: A tutorial. Proc. IEEE 76 (1988), 212–232
[8] Dugard L., Verriest E. I.: Stability and Control of Time-Delay Systems. (Lecture Notes in Control and Information Sciences 228.) Springer Verlag, Berlin 1997 MR 1482570 | Zbl 0901.00019
[9] El–Khazaly R.: Variable structure robust control of uncertain time-delay systems. Automatica 34 (1998), 3, 327–332 DOI 10.1016/S0005-1098(97)00200-8 | MR 1623124
[10] Fiagbedzi Y., Pearson A.: Feedback stabilization of linear autonomous time lag systems. IEEE Trans. Automat. Control 31 (1986), 847–855 DOI 10.1109/TAC.1986.1104417 | MR 0853435 | Zbl 0601.93045
[11] Fliess M.: Generalized controller canonical forms for linear and nonlinear dynamics. IEEE Trans. Autémat. Control 35 (1990), 9, 994–1000 MR 1065035 | Zbl 0724.93010
[12] Fridman L., Fridman, E., Shustin E.: Steady modes in an autonomous system with break and delay. J. Differential Equations 29 (1993), 8 Zbl 0808.34076
[13] Fridman L., Fridman, E., Shustin E.: Steady modes and sliding modes in the relay control systems with time delay. In: 35th IEEE CDC’96 (Conference on Decision and Control), Kobe 1996, pp. 4601–4606
[14] Gouaisbaut F., Blanco, Y., Richard J.: Robust control of nonlinear time delay system: A sliding mode control design. In: IFAC Symposium NOLCOS’01, St Petersburg 2001. Accepted
[15] Gouaisbaut F., Dambrine, M., Richard J.-P.: Sliding mode control of perturbed systems with time varying delays. In: SCS’01, IFAC Symposium on Structure and Control Systems, Prague 2001
[16] Gouaisbaut F., Perruquetti W., Orlov, Y., Richard J.-P.: A sliding mode controller for linear time delay systems. In: Proc. ECC’99 European Control Conference, Karlsruhe 1999
[17] Gouaisbaut F., Perruquetti W., Richard J.-P.: A sliding mode control for linear systems with input and state delays. In: Proc. CDC’99, 38th Conference on Decision and Control, Phoenix 1999
[18] Goubet–Bartholoméüs A., Dambrine, M., Richard J.-P.: Stability of perturbed systems with time-varying delay. Systems Control Lett. 31 (1997), 155–163 DOI 10.1016/S0167-6911(97)00032-7 | MR 1470693
[19] Kolmanovskii V., Myshkis A.: Applied Theory of Functional Differential Equations (Math. Appl. 85.) Kluwer, Dordrecht 1992 MR 1256486
[20] Kolmanovskii V., Myshkis A.: Introduction to the Theory and Applications of Functional Differential Equations. Kluwer, Dordrecht 1999 MR 1680144 | Zbl 0917.34001
[21] Kolmanovskii V., Niculescu, S., Richard J.-P.: On the Liapunov–Krasovskii functionals for stability analysis of linear delay systems. Internat. J. Control 72 (1999), 4, 374–384 DOI 10.1080/002071799221172 | MR 1675003
[22] Kolmanovskii V., Richard J.-P.: Stability of some linear systems with delay. IEEE Trans. Automat. Control 44 (1999), 5, 984–989 DOI 10.1109/9.763213 | MR 1690541
[23] Li X., Yurkovich S.: Sliding mode control of systems with delayed states and control. Variable Structure Systems, Sliding Mode and Nonlinear Control 247 (1999), 1 MR 1714565
[24] Lukyanov A., Utkin V.: Methods of reducing equations of dynamics systems to regular form. Automat. Remote Control 42 (1981), 413–420
[25] Luo N., Sen M. De la: State feedback sliding mode controls of a class of time-delay systems. In: ACC’92 (American Control Conference), Chicago 1992, pp. 894–895
[26] Luo N., Sen M. De la: State feedback sliding mode control of a class of uncertain time-delay systems. IEE Proceedings-D 140 (1993), 4, 261–274 DOI 10.1049/ip-d.1993.0035
[27] Manitius A., Olbrot A.: Finite spectrum assignment problem for systems with delays. IEEE Trans. Automat. Control 24 (1979), 4, 541–553 DOI 10.1109/TAC.1979.1102124 | MR 0538808 | Zbl 0425.93029
[28] Orlov Y.: Discontinuous unit feedback control of uncertain infinite-dimensional systems. IEEE Trans. Automat. Control 45 (2000), 5, 834–843 DOI 10.1109/9.855545 | MR 1774140 | Zbl 0973.93018
[29] Orlov Y., Utkin V.: Sliding mode control in infinite-dimensional systems. Automatica 6 (1987), 753–757 DOI 10.1016/0005-1098(87)90032-X | MR 0922555 | Zbl 0661.93036
[30] Perruquetti W., Barbot J.: Sliding Mode Control in Engineering. Marcel Dekker, New York 2001. To appear
[31] Richard J.: Some trends and tools for the study of time delay systems. In: 2nd Conference IMACS-IEEE CESA’98, Computational Engineering in Systems Applications, Tunisia 1998, pp. 27–43
[32] Richard J., Kolmanovskii V. E.: Delay systems. Mathematics and Computers in Simulation (Special issue), 45 (1998), 3–4 MR 1622951 | Zbl 1017.93507
[33] Roh Y., Oh J.: Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation. Automatica 35 (1999), 1681–1685 MR 1831769 | Zbl 0931.93015
[34] Shyu K., Yan J.: Robust stability of uncertain time-delay systems and its stabilization by variable structure control. Internat. J. Control 57 (1993), 237–246 DOI 10.1080/00207179308934385 | MR 1201742 | Zbl 0774.93066
[35] Sira–Ramirez H.: Differential geometric methods in variable-structure control. Internat. J. Control 48 (1998), 4, 1359–1390 DOI 10.1080/00207178808906256 | MR 0964768
[36] Tan K., Wang, Q., Lee T.: Finite spectrum assignment control of unstable time delay processes with relay tuning. Ind. Eng. Chem. Res. 37 (1998), 4, 1351–1357 DOI 10.1021/ie970765o
[37] Utkin V.: Sliding Modes in Control Optimization. CCES Springer–Verlag, Berlin 1991 MR 1295845
[38] Zheng F., Cheng, M., Gao W.-B.: Variable structure control of time-delay systems with a simulation study on stabilizing combustion in liquid propellant rocket motors. Automatica 31 (1995), 7, 1031–1037 DOI 10.1016/0005-1098(95)00012-L | MR 1343573 | Zbl 0842.93011
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