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Existence and uniqueness of minimal realizations in the $$C^\infty$$ case. (English) Zbl 0497.93014

##### MSC:
 93B20 Minimal systems representations 93B15 Realizations from input-output data 93C10 Nonlinear systems in control theory 57R27 Controllability of vector fields on $$C^\infty$$ and real-analytic manifolds 57R50 Differential topological aspects of diffeomorphisms 57M10 Covering spaces and low-dimensional topology
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##### References:
 [1] Boothby, W.M., () [2] J.P. Gauthier and G. Bornard, Uniqueness of weakly minimal analytic realisations, submitted for publication. · Zbl 0509.57024 [3] Hermann, R.; Krener, A.J., Nonlinear controllability and observability, IEEE trans. automat. control, 22, 5, (1977) · Zbl 0396.93015 [4] Lobry, C., Bases mathématiques de la théorie des asservissements non linéaires, (1975), Université de Bordeaux [5] Serre, J.P., () [6] Sussmann, H.J., Existence and uniqueness of minimal realisations of nonlinear systems, Math. system theory, 10, 263-284, (1977) [7] Sussmann, H.J., A generalization of the closed subgroup theorem to quotients of an arbitrary manifold, J. differential geometry, 10, 151-166, (1975) · Zbl 0342.58004 [8] Sussmann, H.J., Some properties of vector fields that are not altered by small perturbations, J. differential equations, 292-315, (1976) · Zbl 0346.49036 [9] Sussmann, H.J., On quotient manifolds, a generalization of the closed subgroup theorem, Bull. amer. math. society, 80, 113, (1974) [10] Sussmann, H.J., Orbits of families of vector fields and integrability of distributions, Trans. amer. math. soc., 120, (June 1979)
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