×

zbMATH — the first resource for mathematics

The tracking and regulation problem for a class of generalized systems. (English) Zbl 1274.93096
Summary: 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.
MSC:
93B51 Design techniques (robust design, computer-aided design, etc.)
93B25 Algebraic methods
PDF BibTeX XML Cite
Full Text: Link
References:
[1] Ailon A.: Controllability of generalized linear time-invariant systems. IEEE Trans. Automat. Control AC-32 (1987), 429-432 · Zbl 0622.93007
[2] Ailon A.: An approach for pole assignment in singular systems. IEEE Trans. Automat. Control AC-34 (1989), 889-893 · Zbl 0698.93036
[3] Armentano V. A.: Eigenvalue placement for generalized linear systems. Systems Control Lett. 4 (1984), 199-202 · Zbl 0538.93024
[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 · Zbl 0666.93052
[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 · Zbl 0726.93050
[6] Banaszuk A., Kociecki M., Przyluski K. M.: Implicit linear discrete-time systems. Math. Control, Signals and Systems 3 (1990), xxx-xxx · Zbl 0726.93050
[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 · Zbl 0464.93039
[10] Conte G., Perdon A. M.: Generalized state space realizations of nonproper rational transfer matrices. System Control Lett. 1 (1982), 270-276 · Zbl 0473.93023
[11] Dai L.: Singular Control Systems. (Lecture Notes in Control and Inform. Sci. 118.) Springer-Verlag, Berlin 1989 · Zbl 0669.93034
[12] Dai L.: Observers for discrete-singular systems. IEEE Trans. Automat. Control AC-33 (1990), 187-191 · Zbl 0633.93025
[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 · Zbl 0326.93007
[14] Davison E. J., Goldenberg A.: Robust control of a general servomechanism problem: the servo compensator. Automatica 11 (1975), 461-471 · Zbl 0319.93025
[15] Fletcher L. R., Kautsky, J., Nichols N. K.: Eigenstructure assignment in descriptor systems. IEEE Trans. Automat. Control AC-31 (1986), 1138-1141 · Zbl 0608.93031
[16] Fletcher L. R.: Regularisability of descriptor systems. Internat. J. Systems Sci. 17 (1986), 5, 843-847 · Zbl 0588.93029
[17] Fletcher L. R.: Pole placement and controllability subspaces in descriptor systems. Internat. J. Control 66 (1997), 5, 677-709 · Zbl 0876.93040
[18] Fletcher L. R., Aasaraai A.: On disturbance decoupling in descriptor systems. SIAM J. Control Optim. 27 (1989), 5, 1319-1332 · Zbl 0693.93016
[19] Lewis F. L.: A survey of linear singular systems. Circuits Systems Signal Process. 5 (1986), 3-35 · Zbl 0613.93029
[20] Luenberger D. G.: Time-invariant descriptor systems. Automatica 14 (1978), 473-481 · Zbl 0398.93040
[21] Moylan P. J.: Stable inversion for linear singular systems. IEEE Trans. Automat. Control AC-22 (1977), 74-78 · Zbl 0346.93017
[22] Ozcaldiran K., Lewis F. L.: A geometric approach to eigenstructure assignment for singular systems. IEEE Trans. Automat. Control AC-32 (1987), 629-632 · Zbl 0623.93031
[23] Pandolfi L.: Controllability and stabilizability for linear systems of algebraic and differential equations. J. Optim. Theory Appl. 30 (1980), 601-620 · Zbl 0397.93006
[24] Tan S., Vandewalle J.: Observer design for singular systems using canonical forms. IEEE Trans. Circuits Systems CS-35 (1988), 583-587 · Zbl 0653.93014
[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 · Zbl 0854.93120
[26] Verghese G. C., Levy B., Kailath T.: A generalized state space for singular systems. IEEE Trans. Automat. Control AC-26 (1981), 811-831 · Zbl 0541.34040
[27] Verhaegen M., Dooren P. van: A reduced observer for descriptor systems. System Control Lett. 8 (1986), 29-37 · Zbl 0598.93006
[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 · Zbl 0612.93028
[29] Yip E., Sincovec R. F.: Solvability, controllability and observability of continuous descriptor systems. IEEE Trans. Automat. Control AC-26 (1981), 702-707 · Zbl 0482.93013
[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 · Zbl 0612.93030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.