Fliess, M. Controllability revisited. (English) Zbl 0777.93005 Mathematical system theory, Festschr. Honor R. E. Kalman 60th Birthd., 463-474 (1991). Summary: [For the entire collection see Zbl 0742.00029.]Kalman’s controllability is extended to nonlinear dynamics via elementary differential field techniques. This generalization, which was first suggested by J.-F. Pommaret, is related to the notion of strong accessibility introduced by H. J. Sussmann and V. Jurdjevic [J. Diff. Equations 12, 95-116 (1972; Zbl 0242.49040)]. In the case of constant or time-varying linear systems, it comes down to a purely module-theoretic description. As a bonus of our methods we give a straightforward characterization of hidden modes and we also demonstrate that the controllability of a nonlinear dynamics is equivalent to the controllability of its tangent linearized dynamics. Cited in 5 Documents MSC: 93B05 Controllability 93C10 Nonlinear systems in control theory Keywords:Kalman’s controllability; strong accessibility Citations:Zbl 0742.00029; Zbl 0242.49040 PDFBibTeX XMLCite \textit{M. Fliess}, in: Mathematical system theory. The influence of R. E. Kalman. A Festschrift in honor of Professor R. E. Kalman on the occasion of his 60th birthday. Berlin etc.: Springer-Verlag. 463--474 (1991; Zbl 0777.93005)