×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
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)
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.