Sliding mode control in the presence of delay
Kybernetika, Tome 37 (2001) no. 3, pp. 277-294 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 93B12, 93B50, 93C23
Keywords: relay-delay system; sliding mode controllers; input delay; state delay
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Richard, Jean-Pierre; Gouaisbaut, Fréderic; Perruquetti, Wilfrid. Sliding mode control in the presence of delay. Kybernetika, Tome 37 (2001) no. 3, pp. 277-294. http://geodesic.mathdoc.fr/item/KYB_2001_37_3_a5/

[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 | MR | Zbl

[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

[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 | Zbl

[9] El–Khazaly R.: Variable structure robust control of uncertain time-delay systems. Automatica 34 (1998), 3, 327–332 | DOI | MR

[10] Fiagbedzi Y., Pearson A.: Feedback stabilization of linear autonomous time lag systems. IEEE Trans. Automat. Control 31 (1986), 847–855 | DOI | MR | Zbl

[11] Fliess M.: Generalized controller canonical forms for linear and nonlinear dynamics. IEEE Trans. Autémat. Control 35 (1990), 9, 994–1000 | MR | Zbl

[12] Fridman L., Fridman, E., Shustin E.: Steady modes in an autonomous system with break and delay. J. Differential Equations 29 (1993), 8 | Zbl

[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 | MR

[19] Kolmanovskii V., Myshkis A.: Applied Theory of Functional Differential Equations (Math. Appl. 85.) Kluwer, Dordrecht 1992 | MR

[20] Kolmanovskii V., Myshkis A.: Introduction to the Theory and Applications of Functional Differential Equations. Kluwer, Dordrecht 1999 | MR | Zbl

[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 | MR

[22] Kolmanovskii V., Richard J.-P.: Stability of some linear systems with delay. IEEE Trans. Automat. Control 44 (1999), 5, 984–989 | DOI | MR

[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

[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

[27] Manitius A., Olbrot A.: Finite spectrum assignment problem for systems with delays. IEEE Trans. Automat. Control 24 (1979), 4, 541–553 | DOI | MR | Zbl

[28] Orlov Y.: Discontinuous unit feedback control of uncertain infinite-dimensional systems. IEEE Trans. Automat. Control 45 (2000), 5, 834–843 | DOI | MR | Zbl

[29] Orlov Y., Utkin V.: Sliding mode control in infinite-dimensional systems. Automatica 6 (1987), 753–757 | DOI | MR | Zbl

[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 | Zbl

[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 | Zbl

[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 | MR | Zbl

[35] Sira–Ramirez H.: Differential geometric methods in variable-structure control. Internat. J. Control 48 (1998), 4, 1359–1390 | DOI | MR

[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

[37] Utkin V.: Sliding Modes in Control Optimization. CCES Springer–Verlag, Berlin 1991 | MR

[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 | MR | Zbl