Previous |  Up |  Next


state feedback controller; time-delay
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.
[1] Bernstein D. S., Michel A. N.: Special issue: Saturating actuators. Internat. J. Robust and Nonlinear Control 5 (1995), 375–380 MR 1346405
[2] Siljak D. D.: Large Scale System: Stability and Structure. North Holland, New York 1978 MR 0595867
[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 10.1080/00207178808906058 | MR 0935055 | Zbl 0636.93063
[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 1482570 | Zbl 0901.00019
[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 10.1109/9.769385 | MR 1689146
[6] Hennet J. C., Tarbouriech S.: Stability and stabilization of delay differential systems. Automatica 33 (1997), 347–354 DOI 10.1016/S0005-1098(96)00185-9 | MR 1442553 | Zbl 0889.93049
[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 10.1109/9.412630 | MR 1347839 | Zbl 0835.93048
[8] Kapila V., Haddad W. M.: Robust stabilization for systems with parametric uncertainty and time delay. J. Franklin Inst. 336 (1999), 473–480 MR 1680229 | Zbl 0978.93068
[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 10.1109/9.489216 | MR 1387004 | Zbl 0851.93067
[13] Petersen I. R.: A stabilization algorithm for a class of uncertain linear systems. Systems Control Lett. 8 (1987), 351–357 DOI 10.1016/0167-6911(87)90102-2 | MR 0884885 | Zbl 0618.93056
[14] Stoorvogel A. A., Saberi A.: Special issue: Control problems with constraints. Internat. J. Robust and Nonlinear Control 9 (1999), 583–717 MR 1712282
[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 10.1002/(SICI)1099-1239(199709)7:9<835::AID-RNC216>3.0.CO;2-P | MR 1470370 | Zbl 0888.93050
[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 1482584
[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
Partner of
EuDML logo