Willems, Jan C. Input-output and state-space representations of finite-dimensional linear time-invariant systems. (English) Zbl 0507.93017 Linear Algebra Appl. 50, 581-608 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 40 Documents MSC: 93B20 Minimal systems representations 93B15 Realizations from input-output data 93B25 Algebraic methods 93C05 Linear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations 93C99 Model systems in control theory 93A05 Axiomatic systems theory Keywords:polynomial matrices; system matrices; realization theory; almost invariant subspaces × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Willems, J. C., System theoretic models for the analysis of physical systems, Ricerche di Automatica, 10, 2, 71-106 (1979), (Special Issue on Systems Theory and Physics) · Zbl 0938.37525 [2] Willems, J. C., Modeling and representation of dynamical systems defined in terms of external variables, Proceedings of the 20th IEEE Conference on Decision and Control, 1326-1330 (1981) [3] Fuhrmann, P. A., Algebraic system theory: an analyst’s point of view, J. Franklin Inst., 301, 521-540 (1976) · Zbl 0332.93001 [4] Rosenbrock, H. H., State Space and Multivariable Theory (1970), Wiley: Wiley New York · Zbl 0246.93010 [5] Wolovich, W. A., Linear Multivariable Systems (1974), Springer: Springer New York · Zbl 0291.93002 [6] Kailath, T., Linear Systems (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0458.93025 [7] Wonham, W. M., Linear Multivariable Control: A Geometric Approach (1979), Springer: Springer New York · Zbl 0393.93024 [8] Willems, J. C., Almost invariant subspaces: an approach to high gain feedback design—Part 1: Almost controlled invariant subspaces, IEEE Trans. Automat. Control, AC-26, 235-252 (1981) · Zbl 0463.93020 [9] Hautus, M. L.J.; Silverman, L. M., System structure and singular control, Linear Algebra Appl., 50, 369-402 (1983) · Zbl 0522.93021 [10] Brockett, R. W., Control theory and analytical mechanics, (Martin, C.; Hermann, R., Geometric Control Theory (1977), Math. Sci. Press. Brookline: Math. Sci. Press. Brookline Mass), 1-46 · Zbl 0368.93002 [11] van der Schaft, A. J., System theoretic descriptions of physical systems, (Doctoral Diss. (1983), Mathematics Dept., Univ. of Groningen: Mathematics Dept., Univ. of Groningen The Netherlands) · Zbl 0546.93001 [12] Martin, C.; Hermann, R., Applications of algebraic geometry to systems theory: The McMillan degree and Kronecker indices of transfer functions as topological and holomorphic s ystem invariants, SIAM J. Control and Optim., 16, 743-755 (1978) · Zbl 0401.93020 [13] Kalman, R. E.; Falb, P. L.; Arbib, M., Topics in Mathematical System Theory (1969), McGraw-Hill · Zbl 0231.49001 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.