Title:
|
New trends in design of observers for time-delay systems (English) |
Author:
|
Sename, Olivier |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
37 |
Issue:
|
4 |
Year:
|
2001 |
Pages:
|
[427]-458 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
This paper presents some recent results about the design of observers for time-delay systems. It is focused on methods that can lead to design some useful observers in practical situations. First the links between observability properties and observers design is emphasized. Then some necessary and sufficient conditions and a method are provided to obtain unknown input observers for time-delay systems. Furthermore some $H_{\infty }$ design using Lyapunov–Krasovskii and Lyapunov–Razumikhin theories are presented and compared. Finally a polynomial approach based on the parametrization of all observers is proposed that allows to design robust observers for systems including unstructured uncertainties. (English) |
Keyword:
|
time-delay system |
Keyword:
|
observability |
MSC:
|
90-02 |
MSC:
|
93B07 |
MSC:
|
93B51 |
MSC:
|
93C23 |
idZBL:
|
Zbl 1265.93108 |
idMR:
|
MR1859095 |
. |
Date available:
|
2009-09-24T19:40:53Z |
Last updated:
|
2015-03-26 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135420 |
. |
Reference:
|
[1] Chen J., Patton R. J.: Robust model-based fault diagnosis for dynamic systems.Kluwer Academic Publishers, Dordrecht 1999 Zbl 0920.93001 |
Reference:
|
[2] Choi H. H., Chung M. J.: Observer-based $H_{\infty }$ controller design for state delayed linear systems.Automatica 32 (1996), 7, 1073–1075 MR 1405466, 10.1016/0005-1098(96)00014-3 |
Reference:
|
[3] Choi H. H., Chung M. J.: Robust observer-based $H_{\infty }$ controller design for linear uncertain time-delay systems.Automatica 33 (1997), 9, 1749–1752 MR 1481837 |
Reference:
|
[5] Darouach M., Zasadzinski, M., Xu S. J.: Full order observers for linear systems with unknown inputs.IEEE Trans. Automat. Control 39 (1994), 3, 606–609 Zbl 0813.93015, MR 1268304, 10.1109/9.280770 |
Reference:
|
[6] DeSouza C. E., Palhares R. M., Peres P. L. D.: Robust $H_\infty $ filtering for uncertain linear systems with multiple time-varying state delays: An LMI approach.In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 2023–2028 |
Reference:
|
[7] Dugard L., (eds) E. I. Verriest: Stability and Control of Time-delay Systems.(Lecture Notes in Control and Inform. Sci. 228.) Springer Verlag, Berlin 1998 MR 1482570 |
Reference:
|
[8] Eising R.: Pole assignment for systems over rings.Systems Control Lett. 2 (1982), 1, 225–229 Zbl 0519.93033, MR 0690234, 10.1016/0167-6911(82)90006-8 |
Reference:
|
[9] Emre E., Khargonekar P. P.: Regulation of split linear systems over rings: Coefficient-assignment and observers.IEEE Trans. Automat. Control 27 (1982), 1, 104–113 Zbl 0502.93019, MR 0673076, 10.1109/TAC.1982.1102815 |
Reference:
|
[10] Fattouh A.: Robust Observation and Digital Control for Systems with Time-delays (in French).Ph. D. Thesis, I.N.P.G – Laboratoire d’Automatique de Grenoble, Grenoble 2000 |
Reference:
|
[11] Fattouh A., Sename, O., Dion J.–M.: $H_{\infty }$ observer design for time-delay systems.In: Proc. 37th IEEE Conference on Decision and Control, Tampa 1998, pp. 4545–4546 |
Reference:
|
[12] Fattouh A., Sename, O., Dion J.–M.: Robust observer design for time-delay systems: A Riccati equation approach.Kybernetika 35 (1999), 6, 753–764 MR 1747974 |
Reference:
|
[13] Fattouh A., Sename, O., Dion J.–M.: An unknown input observer design for linear time-delay systems.In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 4222–4227 |
Reference:
|
[14] Fattouh A., Sename, O., Dion J.–M.: $H_\infty $ controller and observer design for linear systems with point and distributed time-delays: An LMI approach.In: 2nd IFAC Workshop on Linear Time Delay Systems, Ancône 2000 |
Reference:
|
[15] Fattouh A., Sename, O., Dion J.–M.: An LMI approach to robust observer design for linear time-delay systems.In: Proc. 39th IEEE Conference on Decision and Control, Sydney 2000 |
Reference:
|
[16] Fattouh A., Sename, O., Dion J.–M.: Robust observer design for linear uncertain time-delay systems: A factorization approach.In: 14th Internat. Symposium on Mathematical Theory of Networks and Systems, Perpignan 2000 |
Reference:
|
[17] Fiagbedzi Y. A., Pearson A. E.: Exponential state observer for time-lag systems.Internat. J. Control 51 (1990), 1, 189–204 Zbl 0695.93086, MR 1035873, 10.1080/00207179008934056 |
Reference:
|
[18] Habets L.: Algebraic and Computational Aspects of Time-delay Systems.Ph. D. Thesis, Eindhoven University of Technology 1994 Zbl 0804.93031, MR 1276720 |
Reference:
|
[19] Hou M., Müller P. C.: Design of observers for linear systems with unknown inputs.IEEE Trans. Automat. Control 37 (1992), 6, 871–875 Zbl 0775.93021, MR 1164570, 10.1109/9.256351 |
Reference:
|
[20] Ivanescu D., Snyder A. F., Dion J.–M., Dugard L., Georges, D., Hadjsaid N.: Robust stabilizing controller for an interconnected power system: A time delay approach.In: 14th Internat. Symposium on Mathematical Theory of Networks and Systems, Perpignan 2000 |
Reference:
|
[21] Jankovic M., Kolmanovsky I.: Controlling nonlinear systems through time-delays: an automotive perspective.In: Proc. 8th European Control Conference ECC’99, Karlsruhe 1999 |
Reference:
|
[22] Kamen E. W., Khargonekar P. P., Tannenbaum A.: Proper stable Bezout factorizations and feedback control of linear time-delay systems.Internat. J. Control 43 (1986), 3, 837–857 Zbl 0599.93047, MR 0828360, 10.1080/00207178608933506 |
Reference:
|
[23] Kučera V.: Discrete Linear Control: The Polynomial Equation Approach.Wiley, Chichester 1979 Zbl 0432.93001, MR 0573447 |
Reference:
|
[24] Lee E.B., Lu W. S.: Coefficient assignability for linear systems with delays.IEEE Trans. Automat. Control AC-29 (1984), 128–131 Zbl 0561.93025, MR 0764706 |
Reference:
|
[25] Lee E. B., Olbrot A. W.: Observability and related structural results for linear hereditary systems.Internat. J. Control 34 (1981), 1061–1078 Zbl 0531.93015, MR 0643872, 10.1080/00207178108922582 |
Reference:
|
[26] Lee E. B., Zak S. H.: On spectrum placement for linear time-invariant delay systems.IEEE Trans. Automat. Control AC-27 (1982), 446–449 Zbl 0492.93019, MR 0680110, 10.1109/TAC.1982.1102931 |
Reference:
|
[27] Lee J. H., Kim S. W., Kwon W. H.: Memoryless $h^{\infty }$ controllers for state delayed systems.IEEE Trans. Automat. Control 39 (1994), 1, 159–162 MR 1258692, 10.1109/9.273356 |
Reference:
|
[29] Manitius A., Triggiani R.: Function space controllability of linear retarded systems: A derivation from abstract operator conditions.SIAM J. Control Optim. 16 (1978), 4, 599–645 Zbl 0442.93009, MR 0482505, 10.1137/0316041 |
Reference:
|
[30] Morse A. S.: Ring models for delay differential systems.Automatica 12 (1976), 529–531 Zbl 0345.93023, MR 0437162, 10.1016/0005-1098(76)90013-3 |
Reference:
|
[31] Niculescu S. I.: On the stability and stabilization of linear systems with delayed-state (in French).Ph. D. Thesis, Laboratoire d’Automatique de Grenoble, INPG, 1996 |
Reference:
|
[32] Niculescu S. I., Trofino–Neto A., Dion, J.–M., Dugard L.: Delay-dependent stability of linear systems with delayed state: An l.m.i. approach. In: Proc. 34th Conference on Decision and Control, New Orleans 1995, pp. 1495–1496 |
Reference:
|
[33] Nobuyama E., Kitamori T.: Spectrum assignment and parameterization of all stabilizing compensators for time-delay systems.In: Proc. 29th Conference on Decision and Control, Honolulu 1990, pp. 3629–3634 |
Reference:
|
[34] Pearson A. E., Fiagbedzi Y. A.: An observer for time lag systems.IEEE Trans. Automat. Control 34 (1989), 7, 775–777 Zbl 0687.93011, MR 1000675, 10.1109/9.29412 |
Reference:
|
[35] Picard P., Lafay J. F., Kučera V.: Feedback realization of nonsingular precompensators for linear systems with delays.IEEE Trans. Automat. Control 42 (1997), 6, 848–852 Zbl 0888.93029, MR 1455716, 10.1109/9.587342 |
Reference:
|
[36] Picard P., Sename, O., Lafay J. F.: Observers and observability indices for linear systems with delays.In: CESA 96, IEEE Conference on Computational Engineering in Systems Applications, volume 1, Lille 1996, pp. 81–86 |
Reference:
|
[37] Pourboghrat F., Chyung D. H.: Exact state-variable reconstruction of delay systems.Internat. J. Control 44 (1986), 3, 867–877 Zbl 0603.93008, MR 0850351, 10.1080/00207178608933637 |
Reference:
|
[38] Richard S., Chevrel, P., Maillard B.: Active control of future vehicle drivelines.In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 3752–3767 |
Reference:
|
[39] Salamon D.: Observers and duality between observation and state feedback for time delay systems.IEEE Trans. Automat. Control 25 (1980), 6, 1187–1192 Zbl 0471.93011, MR 0601503, 10.1109/TAC.1980.1102507 |
Reference:
|
[41] Sename O.: Unknown input robust observers for time-delay systems.In: 36th IEEE Conference on Decision and Control, San Diego 1997, pp. 1629–1630 |
Reference:
|
[42] Sename O., Lafay J. F., Rabah R.: Controllability indices of linear systems with delays.Kybernetika 6 (1995), 559–580 Zbl 0864.93023, MR 1374145 |
Reference:
|
[43] Sontag E. D.: Linear systems over commutative rings; a survey.Ricerche Automat. 7 (1976), 1–16 |
Reference:
|
[44] Su J.-H.: Further results on the robust stability of linear systems with a single time delay.Systems Control Lett. 23 (1994), 375–379 Zbl 0805.93045, MR 1303587, 10.1016/0167-6911(94)90071-X |
Reference:
|
[45] Tornambè A.: Simple observer-based control law for time lag systems.Internat. J. Systems Sci. 23 (1992), 9, 1463–1473 Zbl 0781.93045, MR 1181805, 10.1080/00207729208949399 |
Reference:
|
[46] Wang Z., Huang, B., Unbehauen H.: Robust $H_{\infty }$ observer design for uncertain time-delay systems: (i) the continuous-time case.In: IFAC 14th World Congress, Beijing 1999, pp. 231–236 |
Reference:
|
[47] Watanabe K.: Finite spectrum assignment and observer for multivariable systems with commensurate delays.IEEE Trans. Automat. Control AC-31 (1986), 6, 543–550 Zbl 0596.93009, MR 0839083, 10.1109/TAC.1986.1104336 |
Reference:
|
[48] Watanabe K., Ouchi T.: An observer of systems with delays in state variables.Internat. J. Control 41 (1985), 1, 217–229 MR 0775229, 10.1080/0020718508961121 |
Reference:
|
[49] Wonham W. M.: Linear Multivariable Control: A Geometric Approach.Springer Verlag, New York 1979 Zbl 0609.93001, MR 0569358 |
Reference:
|
[50] Yao Y. X., Zhang Y. M., Kovacevic R.: Parameterization of observers for time delay systems and its application in observer design.IEE Proc. – Control Theory Appl. 143 (1996), 3, 225–232 |
Reference:
|
[51] Yao Y. X., Zhang Y. M., Kovacevic R.: Functional observer and state feedback for input time-delay systems.Internat. J. Control 66 (1997), 4, 603–617 Zbl 0873.93015, MR 1673792, 10.1080/002071797224612 |
. |