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Categorical approach to nonlinear constant continuous-time systems. (English) Zbl 0417.93008

93A10 General systems
93B25 Algebraic methods
93B05 Controllability
93B07 Observability
93B20 Minimal systems representations
93C99 Model systems in control theory
Full Text: EuDML
[1] 1. M. A. ARBIB and E. G. MANES, Foundations of System Theory: Decomposable Systems, C.O.I.N.S. Technical Report 73-B3, Univ. of Mass., Amherst, 1973. MR490084 · Zbl 0294.93002
[2] 2. M. A. ARBIB and E. G. MANES, Fuzzy Machines in a Category, C.O.I.N.S. Technical Report 75-B1, Univ. of Mass., Amherst, 1975. MR407106 · Zbl 0318.18008
[3] 3. H. EHRIG, K. D. KIERMEIER, H.-J. KREOWSKI and W. KÜHNEL, Universal Theory of Automata: A Categorical Approach, Teubner-Verlag, Stuttgart, 1974. Zbl0289.94023 MR382387 · Zbl 0289.94023
[4] 4. H. EHRIG and H.-J. KREOWSKI, The Skeleton of Minimal Realization, Technical Report 76-04, Technische Universität Berlin, 1976, to appear in Studien zur Algebra und ihre Anwendungen, Akademie-Verlag, Berlin. Zbl0375.93006 MR569582 · Zbl 0375.93006
[5] 5. H. EHRIG and W. KÜHNEL, Topological Automata, R.A.I.R.O., Vol. 8, R-3, 1974, pp. 73-91. Zbl0355.94064 MR360739 · Zbl 0355.94064 · eudml:92013
[6] 6. S. J. HEGNER, A Categorical Approach to Continuous-Time Linear Systems, C.O.I.N.S. Technical Report 76-8, Univ. of Mass., Amherst, 1976.
[7] 7. R. E. KALMAN, P. L. FALB and M. A. ARBIB, Topics in Mathematical System Theory, McGraw-Hill, New York, 1969. Zbl0231.49001 MR255260 · Zbl 0231.49001
[8] 8. S. MACLANE, Categories for the Working Mathematician, Springer-Verlag, Berlin-Heidelberg-New York, 1972. MR1712872 · Zbl 0705.18001
[9] 9. M. PFENDER, Universal Algebra in S-monoidal Categories, Ber. Math. Sem. Univ. München, 20 1974. Zbl0326.18003 · Zbl 0326.18003
[10] 10. H. J. SUSSMANN, Minimal Realizations and Canonical Forms for Bilinear Systems, Research Report, Rutgers Univ., 1975. MR429197
[11] 11. H. J. SUSSMANN, Existence and Uniqueness of Minimal Realizations of Nonlinear Systems, Math. Syst. Theory, Vol. 10, 1977, pp. 263-284. Zbl0354.93017 MR437158 · Zbl 0354.93017 · doi:10.1007/BF01683278
[12] 12. H. J. SUSSMANN, Semigroup Representation, Bilinear Approximation of Input-Output Maps and Generalized Inputs, Research Report, Rutgers Univ., 1975. MR683616
[13] 13. H. J. SUSSMANN, A Generalization of the Closed Subgroup Theorem to Quotients of Arbitrary Manifolds, J. Diff. Geom., Vol. 10, 1975, pp. 151-166. Zbl0342.58004 MR426015 · Zbl 0342.58004
[14] 14. R. VALK, Realisierung allgemeiner Systeme, Berichte der Gesellschaft für Mathematik und Datenverarbeitung, No. 107, Bonn, 1976. Zbl0343.93004 MR496886 · Zbl 0343.93004
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