zbMATH — the first resource for mathematics

Structural properties of singular systems. (English) Zbl 0806.93005
For singular, time-invariant, multivariable, finite-dimensional systems of the form \[ E\dot x(t)= Ax(t)+ Bu(t), \qquad y(t)= Cx(t) \] various notions of controllability resp. reachability and observability resp. reconstructibility are characterized via the geometric approach; the finite as well as the infinite time interval is considered.

93B05 Controllability
93C05 Linear systems in control theory
93B07 Observability
93A10 General systems
Full Text: Link EuDML
[1] A. Banaszuk M. Kociecki, K. M. Pryluski: Remarks on duality between observation and control for implicit linear discrete-time systems. Proceedings of IFAC Workshop System Structure and Control, Prague 1989, pp. 257-260.
[2] U. Baser, K. Ozgaldiran: Observability and regularizability by output injection of the descriptor systems. Circuits Systems Signal Process. 11 (1992), 3, 421-430.
[3] M. E. Bonilla, M. Malabre: Non observable and redundant spaces for implicit descriptions. Proceedings of 30th CDC, Brighton, England, pp. 1425-1430.
[4] J. D. Cobb: Controllability, observability and duality in singular systems. IEEE Trans. Automat. Control AC-26 (1984), 1076-1082.
[5] G. Doetsch: Introduction to the Theory and Application of the Laplace Transformation. Springer-Verlag, Berlin 1974. · Zbl 0278.44001
[6] L. Haliloglu: Reachabililty, controllability and observability in generalized linear time-invariant systems. M.S. Thesis, Dept. Elect. Engng., Bogazicj University, Istanbul 1991.
[7] F. L. Lewis: A tutorial on the geometric analysis of linear time-invariant implicit systems. Automatica 28(1992), 1, 119-137. · Zbl 0745.93033 · doi:10.1016/0005-1098(92)90012-5
[8] M. Malabre: Generalized linear systems: geometric and structural approaches. Linear Algebra Appl. 122-124 (1989), 591-621. · Zbl 0679.93048 · doi:10.1016/0024-3795(89)90668-X
[9] K. Ozcaldiran: Control of Descriptor Systems. Ph. D. Thesis, Georgia Institute of Technology, Atlanta, Ga. 1985. · Zbl 0606.93017
[10] K. Ozgaldiran: A geometric characterization of the reachable and controllable subspaces of descriptor systems. Circuits Systems Signal Process. 5 (1986), 37-48. · Zbl 0606.93017
[11] K. Ozgaldiran: A complete classification of controllable singular systems. Preprint, 1989.
[12] K. Ozcaldiran, F. L. Lewis: On the regularizability of singular systems. IEEE Trans. Automat. Control AC-35 (1990), 1156-1160. · Zbl 0724.93011 · doi:10.1109/9.58561
[13] K. Ozcaldiran: Some generalized notions of observability. Proceedings of the 29th CDC, Honolulu, Hawai 1990, pp. 3635-3639.
[14] L. Schwartz: Mathematics for the Physical Sciences. Hermann, Paris 1966. · Zbl 0151.34001
[15] J.C. Willems: Almost invariant subspaces: An approach to high gain feedback design. Part I: Almost controlled invariant subspaces. IEEE Trans. Automat. Control AC-26 (1981), 235-252. · Zbl 0463.93020 · doi:10.1109/TAC.1981.1102551
[16] A. H. Zemanian: Distribution Theory and Transform Analysis. Dover Publications, New York 1965. · Zbl 0127.07201
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.