×

zbMATH — the first resource for mathematics

A simple definition of hidden modes, poles and zeros. (English) Zbl 0746.93037
Summary: Simple definitions of hidden modes, poles and multivariable constant linear systems are given by means of elementary module theory.

MSC:
93C05 Linear systems in control theory
93B05 Controllability
93C35 Multivariable systems, multidimensional control systems
93B07 Observability
PDF BibTeX XML Cite
Full Text: Link EuDML
References:
[1] H. Blomberg, R. Ylinen: Algebraic Theory of Multivariate Linear Systems. Academic Press, London 1983. · Zbl 0556.93016
[2] F. M. Callier, C A. Desoer: Multivariable Feedback Systems. Springer-Verlag, New York 1982. · Zbl 0248.93017
[3] G. Conte, A. M. Perdon: Zeros, poles and modules in linear system theory. Three Decades of Mathematical System Theory - A Collection of Surveys at the Occasion of the 50th Birthday of J. C Willems (H. Nijmeijer and J. M. Schumacher; Lecture Notes Control Inform. Sci. 135), Springer-Verlag, Berlin -Heidelberg-New York, 1989, pp. 79-100. · Zbl 0701.93016
[4] M. Fliess: Automatique et corps differentiels. Forum Math. 1 (1989), 227-238. · Zbl 0701.93048 · doi:10.1515/form.1989.1.227 · eudml:141614
[5] M. Fliess: Generalized linear systems with lumped or distributed parameters. Internat. J. Control 49 (1989), 1989-1999. · Zbl 0684.93001 · doi:10.1080/00207178908961367
[6] M. Fliess: Commandabilite, matrices de transfert et modes caches. C R. Acad. Sci. Paris Ser. I. Math. 1-309 (1989), 847-851. · Zbl 0685.93009
[7] M. Fliess: Geometric interpretation of the zeros and of the hidden modes of a constant linear system via a renewed realization theory. Proc. IFAC Workshop ”System Structure and Control: State-space and Polynomial Methods”, Prague 1989, pp. 209-213.
[8] M. Fliess: Some basic structural properties of generalized linear systems. Systems Control Lett. 75 (1990), 391-396. · Zbl 0727.93024 · doi:10.1016/0167-6911(90)90062-Y
[9] B. A. Francis, W. M. Wonham: The role of transmission zeros in linear multivariable regulators. Internat. J. Control 22 (1975), 657-681. · Zbl 0321.93016 · doi:10.1080/00207177508922111
[10] T. Kailath: Linear Systems. Prentice-Hall, Englewood-Cliffs, N. J. 1980. · Zbl 0454.93001
[11] S. Lang: Algebra. Addison-Wesley, Reading, MA 1965. · Zbl 0193.34701
[12] A. G. J. MacFarlane, N. Karkanias: Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex variable theory. Internat. J. Control 24 (1976), 33-74. · Zbl 0374.93014 · doi:10.1080/00207177608932805
[13] H. H. Rosenbrock: State Space and Multivariable Theory. Nelson, London 1970. · Zbl 0246.93010
[14] C E. Schrader, M. K. Sain: Research on system zeros: A survey. Interr.at. J. Control 50 (1989), 1407-1433. · Zbl 0686.93036 · doi:10.1080/00207178908953438
[15] W. M. Wonham: Linear Multivariable Control: A Geometric Approach. Third edition. Springer-Verlag, New York-Berlin-Heidelberg 1985. · Zbl 0609.93001
[16] B. F. Wyman, M. K. Sain: Module theoretic zero structures for system matrices. SIAM J. Contiol Optim. 25 (1787), 86-99. · Zbl 0617.93010 · doi:10.1137/0325007
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.