A sufficient condition for the transitivity of pseudo-semigroups: Application to system theory. (English) Zbl 0527.93029


93B99 Controllability, observability, and system structure
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
57R50 Differential topological aspects of diffeomorphisms
54D05 Connected and locally connected spaces (general aspects)
54H20 Topological dynamics (MSC2010)
58A05 Differentiable manifolds, foundations
93C55 Discrete-time control/observation systems
93C99 Model systems in control theory
Full Text: DOI


[1] {\scR. W. Brockett}, On the algebraic structure of bilinear systems, in “Theory and Applications of Variable Structure Systems” (Mohler and Ruberti, Eds.) Academic Press, New York.
[2] Haefliger, A, Structures feuilletées et… groupoïdes, Comm. math. helv., 32, 249-329, (1958) · Zbl 0085.17303
[3] {\scKobayashi-Nomizu}, “Foundations of Differential Geometry,” Vol. I, Interscience, New York.
[4] {\scKuranishi}, Lectures on exterior differential systems.
[5] {\scY. Rouchaleau}, “Linear Discrete Time Finite Dimensionnal Dynamical Systems over Some Classes of Commutative Rings,” Ph.D. Dissertation, Stanford.
[6] Singer-Sternberg, The infinite groups of Lie and Cartan, J. analyse math., 15, 1-114, (1965) · Zbl 0277.58008
[7] {\scE. D. Sonntag}, “Polynomial Response Maps.” Lecture Notes in Control and Information Science No. 13, Springer-Verlag, Berlin/Heidelberg/New York.
[8] Sussmann, H, Some properties… perturbation, J. differential eq., 20, 292-315, (1976) · Zbl 0346.49036
[9] Sussmann, H, Orbits of families of vector fields and integrability of distributions, Trans. amer. math. soc., 180, 171-188, (1973) · Zbl 0274.58002
[10] Sussmann, H, A generalisation of the closed… manifolds, J. differential geometry, 10, 151-166, (1975) · Zbl 0342.58004
[11] Tanaka, N, On differential systems… pseudo-groups, J. math. Kyoto univ., 10, 1-82, (1970) · Zbl 0206.50503
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.