The tracking and regulation problem for a class of generalized systems
Kybernetika, Tome 34 (1998) no. 6, pp. 635-654
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The tracking and regulation problem is considered for a class of generalized systems, in case of exponential reference signals and of disturbance functions. First, the notions of steady-state response and of blocking zero, which are classical for linear time-invariant systems, are given for generalized systems. Then, the tracking and regulation problem is stated and solved for the class of generalized systems under consideration, giving a general design procedure. As a corollary of the effectiveness proof of the design procedure, an algebraic version of the internal model principle is stated for generalized systems.
The tracking and regulation problem is considered for a class of generalized systems, in case of exponential reference signals and of disturbance functions. First, the notions of steady-state response and of blocking zero, which are classical for linear time-invariant systems, are given for generalized systems. Then, the tracking and regulation problem is stated and solved for the class of generalized systems under consideration, giving a general design procedure. As a corollary of the effectiveness proof of the design procedure, an algebraic version of the internal model principle is stated for generalized systems.
Classification : 93B25, 93B50, 93B51, 93C15
Keywords: tracking and regulation problem; linear time-invariant system; design procedure; internal model principle
@article{KYB_1998_34_6_a3,
     author = {Tornamb\`e, Antonio},
     title = {The tracking and regulation problem for a class of generalized systems},
     journal = {Kybernetika},
     pages = {635--654},
     year = {1998},
     volume = {34},
     number = {6},
     mrnumber = {1695368},
     zbl = {1274.93096},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1998_34_6_a3/}
}
TY  - JOUR
AU  - Tornambè, Antonio
TI  - The tracking and regulation problem for a class of generalized systems
JO  - Kybernetika
PY  - 1998
SP  - 635
EP  - 654
VL  - 34
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_1998_34_6_a3/
LA  - en
ID  - KYB_1998_34_6_a3
ER  - 
%0 Journal Article
%A Tornambè, Antonio
%T The tracking and regulation problem for a class of generalized systems
%J Kybernetika
%D 1998
%P 635-654
%V 34
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_1998_34_6_a3/
%G en
%F KYB_1998_34_6_a3
Tornambè, Antonio. The tracking and regulation problem for a class of generalized systems. Kybernetika, Tome 34 (1998) no. 6, pp. 635-654. http://geodesic.mathdoc.fr/item/KYB_1998_34_6_a3/

[1] Ailon A.: Controllability of generalized linear time–invariant systems. IEEE Trans. Automat. Control AC-32 (1987), 429–432 | DOI | MR | Zbl

[2] Ailon A.: An approach for pole assignment in singular systems. IEEE Trans. Automat. Control AC-34 (1989), 889–893 | DOI | MR | Zbl

[3] Armentano V. A.: Eigenvalue placement for generalized linear systems. Systems Control Lett. 4 (1984), 199–202 | DOI | MR | Zbl

[4] Banaszuk A., Kociecki M., Przyluski K. M.: On almost invariant subspaces for implicit linear discrete-time systems. Systems Control Lett. 11 (1988), 289–297 | DOI | MR | Zbl

[5] Banaszuk A., Kociecki M., Przyluski K. M.: The disturbance decoupling problem for implicit linear discrete–time systems. SIAM J. Control Optim. 28 (1990), 1270–1293 | DOI | MR | Zbl

[6] Banaszuk A., Kociecki M., Przyluski K. M.: Implicit linear discrete–time systems. Math. Control, Signals and Systems 3 (1990), xxx–xxx | DOI | MR | Zbl

[7] Campell S. L.: Singular Systems of Differential Equations I. Pitman, New York 1980

[8] Campell S. L.: Singular Systems of Differential Equations II. Pitman, New York 1982

[9] Cobb D.: Feedback and pole placement in descriptor variable systems. Internat. J. Control 33 (1981), 1135–1146 | DOI | MR | Zbl

[10] Conte G., Perdon A. M.: Generalized state space realizations of nonproper rational transfer matrices. System Control Lett. 1 (1982), 270–276 | DOI | MR

[11] Dai L.: Singular Control Systems. (Lecture Notes in Control and Inform. Sci. 118.) Springer–Verlag, Berlin 1989 | MR | Zbl

[12] Dai L.: Observers for discrete-singular systems. IEEE Trans. Automat. Control AC-33 (1990), 187–191 | DOI | MR

[13] Davison E. J.: The robust control of a servomechanism problem for linear time–invariant multivariable systems. IEEE Trans. Automat. Control AC-21 (1976), 25–34 | DOI | MR | Zbl

[14] Davison E. J., Goldenberg A.: Robust control of a general servomechanism problem: the servo compensator. Automatica 11 (1975), 461–471 | DOI | MR | Zbl

[15] Fletcher L. R., Kautsky, J., Nichols N. K.: Eigenstructure assignment in descriptor systems. IEEE Trans. Automat. Control AC-31 (1986), 1138–1141 | DOI | Zbl

[16] Fletcher L. R.: Regularisability of descriptor systems. Internat. J. Systems Sci. 17 (1986), 5, 843–847 | DOI | MR

[17] Fletcher L. R.: Pole placement and controllability subspaces in descriptor systems. Internat. J. Control 66 (1997), 5, 677–709 | DOI | MR

[18] Fletcher L. R., Aasaraai A.: On disturbance decoupling in descriptor systems. SIAM J. Control Optim. 27 (1989), 5, 1319–1332 | DOI | MR

[19] Lewis F. L.: A survey of linear singular systems. Circuits Systems Signal Process. 5 (1986), 3–35 | MR | Zbl

[20] Luenberger D. G.: Time–invariant descriptor systems. Automatica 14 (1978), 473–481 | DOI | Zbl

[21] Moylan P. J.: Stable inversion for linear singular systems. IEEE Trans. Automat. Control AC-22 (1977), 74–78 | DOI | MR

[22] Ozcaldiran K., Lewis F. L.: A geometric approach to eigenstructure assignment for singular systems. IEEE Trans. Automat. Control AC-32 (1987), 629–632 | DOI | Zbl

[23] Pandolfi L.: Controllability and stabilizability for linear systems of algebraic and differential equations. J. Optim. Theory Appl. 30 (1980), 601–620 | DOI | MR

[24] Tan S., Vandewalle J.: Observer design for singular systems using canonical forms. IEEE Trans. Circuits Systems CS-35 (1988), 583–587

[25] Tornambè A.: A simple procedure for the stabilization of a class of uncontrollable generalized systems. IEEE Trans. Automat. Control 41 (1996), 4, 603–607 | DOI | MR | Zbl

[26] Verghese G. C., Levy B., Kailath T.: A generalized state space for singular systems. IEEE Trans. Automat. Control AC-26 (1981), 811–831 | DOI | MR | Zbl

[27] Verhaegen M., Dooren P. van: A reduced observer for descriptor systems. System Control Lett. 8 (1986), 29–37 | DOI

[28] Wang Y. Y., Shi S. J., Zhang Z. J.: Pole placement and compensator design of generalized systems. System Control Lett. 8 (1987), 205–209 | DOI | MR | Zbl

[29] Yip E., Sincovec R. F.: Solvability, controllability and observability of continuous descriptor systems. IEEE Trans. Automat. Control AC-26 (1981), 702–707 | DOI | MR | Zbl

[30] Zhou Z., Shayman M. A., Tarn T. J.: Singular systems: a new approach in the time domain. IEEE Trans. Automat. Control AC-32 (1987), 42–50 | DOI | MR | Zbl