Geodesic
Robust observer design for time-delay systems: a Riccati equation approach
Kybernetika, Tome 35 (1999) no. 6, pp. 753-764 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, a method for $H_\infty $ observer design for linear systems with multiple delays in state and output variables is proposed. The designing method involves attenuating of the disturbance to a pre-specified level. The observer design requires solving certain algebraic Riccati equation. An example is given in order to illustrate the proposed method.
In this paper, a method for $H_\infty $ observer design for linear systems with multiple delays in state and output variables is proposed. The designing method involves attenuating of the disturbance to a pre-specified level. The observer design requires solving certain algebraic Riccati equation. An example is given in order to illustrate the proposed method.
Classification : 93B07, 93B36, 93B51
Keywords: linear system; time delay; Riccati equation; robust observer design 
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     title = {Robust observer design for time-delay systems: a {Riccati} equation approach},
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Fattouh, Anas; Sename, Olivier; Dion, Jean-Michel. Robust observer design for time-delay systems: a Riccati equation approach. Kybernetika, Tome 35 (1999) no. 6, pp. 753-764. http://geodesic.mathdoc.fr/item/KYB_1999_35_6_a7/

[1] Boyd S., Ghaoui L. EL, Feron E., Balakrishnan V.: Linear matrix inequalities in system and control theory. SIAM Stud. Appl. Math. 1994 | MR | Zbl

[2] Choi H. H., Chung M. J.: Observer–based $H_{\infty }$ controller design for state delayed linear systems. Automatica 32 (1996), 1073–1075 | DOI | MR

[3] Choi H. H., Chung M. J.: An LMI approach to $H_{\infty }$ controller design for linear time–delay systems. Automatica 33 (1997), 737–739 | DOI | MR

[4] Fattouh A., Sename O., Dion J.-M.: $H_{\infty }$ Observer design for time–delay systems. In: Proc. of the 37th IEEE Conference on Decision and Control, Tampa 1998, pp. 4545–4546

[5] Fattouh A., Sename O., Dion J.-M.: $\alpha $–decay rate observer design for linear systems with delayed state. In: Proc. of the 8th European Control Conference, Karlsruhe 1999

[6] Furukawa T., Shimemura E.: Stabilizability conditions by memoryless feedback for linear systems with time-delay. Internat. J. Control. 37 (1983), 553–565 | DOI | MR | Zbl

[7] Khargonekar P. P., Petersen I. R., Zhou K.: Robust stabilization of uncertain linear systems: Quadratic stabilizability and $H_\infty $ control theory. IEEE Trans. Automat. Control 35 (1990), 356–361 | DOI | MR

[8] Kolmanovskii V. B., Nosov V. R.: Stability of Functional Differential Equation. Academic Press, New York 1986 | MR

[9] Lee E. B., Olbrot A.: Observability and related structural results for linear hereditary systems. Internat. J. Control. 34 (1981), 1061–1078 | DOI | MR | Zbl

[10] Lee J. H., Kim S. W., Kwon W. H.: Memoryless $H^{\infty }$ controllers for state delayed systems. IEEE Trans. Automat. Control 39 (1994), 159–162 | DOI | MR

[11] 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. of the 34th Conference on Decision and Control, New Orleans 1995, pp. 1495–1496

[12] Pearson A. E., Fiagbedzi Y. A.: An observer for time lag systems. IEEE Trans. Automat. Control 34 (1989), 775–777 | DOI | MR | Zbl

[13] Petersen I. R., Anderson B. D. O., Jonckheere E. A.: A first principles solution to the non–singular $H^\infty $ control problem. Internat. J. Robust and Nonlinear Control 1 (1991), 171–185 | DOI

[14] Ramos J. L., Pearson A. E.: An asymptotic modal observer for linear autonomous time lag systems. IEEE Trans. Automat. Control 40 (1995), 1291–1294 | DOI | MR | Zbl

[15] Watanabe K.: Finite spectrum assignment and observer for multivariable systems with commensurate delays. IEEE Trans. Automat. Control 31 (1986), 543–550 | DOI | MR | Zbl

[16] Watanabe K., Ouchi T.: An observer of systems with delays in state variables. Internat. J. Control 41 (1985), 217–229 | DOI | MR

[17] 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), 225–232

[18] Zhou K., Doyle J. C., Glover K.: Robust and Optimal Control. Prentice–Hall, Englewood Cliffs, N. J. 1996 | Zbl