Geodesic
Nonlinear bounded control for time-delay systems
Kybernetika, Tome 37 (2001) no. 4, pp. 381-396 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A method to derive a nonlinear bounded state feedback controller for a linear continuous-time system with time-delay in the state is proposed. The controllers are based on an $e$-parameterized family of algebraic Riccati equations or on an $e$-parameterized family of LMI optimization problems. Hence, nested ellipsoidal neighborhoods of the origin are determined. Thus, from the Lyapunov–Krasovskii theorem, the uniform asymptotic stability of the closed-loop system is guaranteed and a certain performance level is attained through a quadratic cost function.
A method to derive a nonlinear bounded state feedback controller for a linear continuous-time system with time-delay in the state is proposed. The controllers are based on an $e$-parameterized family of algebraic Riccati equations or on an $e$-parameterized family of LMI optimization problems. Hence, nested ellipsoidal neighborhoods of the origin are determined. Thus, from the Lyapunov–Krasovskii theorem, the uniform asymptotic stability of the closed-loop system is guaranteed and a certain performance level is attained through a quadratic cost function.
Classification : 93B52, 93C10, 93C23, 93D20
Keywords: state feedback controller; time-delay 
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}
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Garcia, Germain; Tarbouriech, Sophie. Nonlinear bounded control for time-delay systems. Kybernetika, Tome 37 (2001) no. 4, pp. 381-396. http://geodesic.mathdoc.fr/item/KYB_2001_37_4_a1/

[1] Bernstein D. S., Michel A. N.: Special issue: Saturating actuators. Internat. J. Robust and Nonlinear Control 5 (1995), 375–380 | MR

[2] Siljak D. D.: Large Scale System: Stability and Structure. North Holland, New York 1978 | MR

[3] Chen B. S., Wang S. S., Lu H. C.: Stabilization of time-delay systems containing saturating actuators. Internat. J. Control 47 (1988), 867–881 | DOI | MR | Zbl

[4] Dugard L., (eds.) E. I. Verriest: Stability and Control of Time-delay Systems. (Lecture Notes in Computer Science 228.), Springer–Verlag, London 1997 | MR | Zbl

[5] Garcia G., Tarbouriech S., Suarez, R., Ramirez J. Alvarez: Nonlinear bounded control for norm-bounded uncertain system. IEEE Trans. Automat. Control 44 (1999), 6, 1254–1258 | DOI | MR

[6] Hennet J. C., Tarbouriech S.: Stability and stabilization of delay differential systems. Automatica 33 (1997), 347–354 | DOI | MR | Zbl

[7] Hmamed A., Benzaouia, A., Bensalah H.: Regulator problem for linear continuous-time delay systems with nonsymmetrical constrained control. IEEE Trans. Automat. Control 40 (1995), 1615–1619 | DOI | MR | Zbl

[8] Kapila V., Haddad W. M.: Robust stabilization for systems with parametric uncertainty and time delay. J. Franklin Inst. 336 (1999), 473–480 | MR | Zbl

[9] Kharitonov V.: Robust stability analysis of time-delay systems: a survey. In: Proc. IFAC Symposium on System Structure and Control, Nantes 1998

[10] Klai M., Tarbouriech, S., Burgat C.: Some independent-time-delay stabilization of linear systems with saturating controls. In: Proc. IEE Control’94, Coventry 1994, pp. 1358–1363

[11] Lafay J. F., Conte G.: Analysis and design methods for delay systems. In: Proc. 34th IEEE Conference on Decision and Control, New Orleans 1995, pp. 2035–2069

[12] Niculescu S.-I., Dion J.-M., Dugard L.: Robust stabilization for uncertain time-delay systems containing saturating actuators. IEEE Trans. Automat. Control 41 (1996), 742–747 | DOI | MR | Zbl

[13] Petersen I. R.: A stabilization algorithm for a class of uncertain linear systems. Systems Control Lett. 8 (1987), 351–357 | DOI | MR | Zbl

[14] Stoorvogel A. A., Saberi A.: Special issue: Control problems with constraints. Internat. J. Robust and Nonlinear Control 9 (1999), 583–717 | MR

[15] Su T. J., Liu P. L., Tsay J. T.: Stabilization of delay-dependence for saturating actuator systems. In: Proc. 30th IEEE Conference on Decision and Control, Brighton 1991, pp. 2891–2892

[16] Suarez R., Alvarez–Ramirez, J., Solis–Daun J.: Linear systems with bounded inputs: global stabilization with eigenvalue placement. Internat. J. Robust and Nonlinear Control 7 (1997), 835–845 | DOI | MR | Zbl

[17] Tarbouriech S.: Local stabilization of continuous-time delay systems with bounded inputs. In: Stability and Control of Time-delay Systems (L. Dugard and E. I. Verriest, eds., Lecture Notes in Computer Science 228), Springer–Verlag, London 1997, pp. 302–317 | MR

[18] Tarbouriech S., Garcia G.: Robust stabilityof uncertain linear delay systems with saturating inputs: an LMI approach. In: Proc. IFAC Symposium on System Structure and Control, Nantes 1998