×

zbMATH — the first resource for mathematics

Solutions to the output regulation problem of linear singular systems. (English) Zbl 0873.93047
Output regulation of linear singular systems is examined for the case when the measurement output is identical to the vector to be regulated. Necessary and sufficient conditions are derived for the regulation problem to be solvable via either full information feedback or error feedback. Explicit construction of the feedback is then given.

MSC:
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
93B52 Feedback control
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Banaszuk, A.; Kociecki, M.; Przyluski, K. M., On almost invariant subspaces for implicit linear discrete-time systems, Syst. & Control Lett., 11, 289-297, (1988) · Zbl 0666.93052
[2] Brenan, K. E.; Campbell, S. L.; Petzold, L. R., Numerical solution of initial-value problems in differential-algebraic equations, (1989), North-Holland Amsterdam · Zbl 0699.65057
[3] Campbell, S. L., Singular systems of differential equations, (1980), Pitman New York · Zbl 0419.34007
[4] Campbell, S. L., Singular systems of differential equations II, (1982), Pitman New York · Zbl 0482.34008
[5] Cobb, D., Controllability, observability, and duality in singular systems, IEEE Trans. Automat. Control, AC-26, 12, 1076-1082, (1984)
[6] Dai, L., Stable and structurally stable regulators for singular systems, Acta Mathematicae Applicatae Sinica, 3, 2, 122-135, (1987) · Zbl 0638.93054
[7] Dai, L., Singular control systems, (Lecture Notes in Control and Information Sciences, Vol. 118, (1989), Springer New York)
[8] El-Tohami, M.; Lovass-Nagy, V.; Powers, D. L., On input function observers for generalized state-space systems, Int. J. Control, 40, 903-922, (1984) · Zbl 0559.93012
[9] Francis, B. A., The linear multivariable regulator problem, SIAM J. Control and Optimization, 15, 3, 486-505, (1977) · Zbl 0382.93025
[10] Knobloch, H. W.; Isidori, A.; Flockerzi, Topics in control theory, (1993), Birkhauser Basel · Zbl 0789.93073
[11] Kucera, V., Model matching of descriptor systems by proportional state feedback, Automatica, 28, 423-426, (1992) · Zbl 0766.93025
[12] Lewis, F. L., Fundamental, reachability, and observability matrices for discrete descriptor systems, IEEE Trans. Automat. Control, AC-30, 502-505, (1985) · Zbl 0557.93011
[13] Lewis, F. L., A survey of linear singular systems, Circuit Syst. Signal Process., 5, 1, 3-36, (1986) · Zbl 0613.93029
[14] Lewis, F. L., A tutorial on the geometric analysis of linear time-invariant implicit systems, Automatica, 28, 1, 119-138, (1992) · Zbl 0745.93033
[15] Lewis, F. L., A review of 2-D implicit systems, Automatica, 28, 2, 345-354, (1992) · Zbl 0766.93035
[16] Luenberger, D. G., Dynamic equations in descriptor form, IEEE Trans. Automat. Control, AC-22, 312-321, (1977) · Zbl 0354.93007
[17] McClamroch, N. H., Singular systems of differential equations as dynamic models for constrained robot systems, (Proc. IEEE Int. Conf. on Robotics and Automation, (1986)), 21-28
[18] Mukundan, R.; Ayawansa, W. D., Feedback control of singular systems—proportional and derivative feedback of the state, Int. J. Syst. Sci., 14, 615-632, (1983) · Zbl 0509.34004
[19] Newcomb, R. W.; Dziurla, B., Some circuits and systems applications of semistate theory, Circuits, Syst. & Signal Process., 8, 4, (1989) · Zbl 0681.94020
[20] Pandolfi, L., Generalized control systems, boundary control systems, and delayed control systems, Math. of Control, Signals, and Syst., 3, 165-181, (1990) · Zbl 0694.93047
[21] Verghese, G. C.; Levy, B. C.; Kailath, T., A generalized state-space for singular systems, IEEE Trans. Automat. Control, AC-26, 811-831, (1981) · Zbl 0541.34040
[22] Willems, J. C., Paradigms and puzzles in the theory of dynamical systems, IEEE Trans. Automat. Control, AC-28, 423-446, (1991)
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.