In this paper we shall describe some recent results that we have obtained on the existence and uniqueness of minimal realizations of finite-dimensional autonomous nonlinear systems• A detailed presentation of these results, with complete proofs and a precise specification of technical assumptions will be given elsewhere (cf. Sussmann 4-and 5). Here we shall limit ourselves to a general outline, and we shall attempt to emphasize the importance of the differential-geometric method which, in our opinion, goes far beyond its mere use as a tool for proving theorems. We believe that, in addition to this important role, the use of Differential Geometry in Systems Theory has other advantages, namely, that it can provide a good framework for the theory, and that it can suggest what are the appropriate questions to be asked, and what kind of answers one should “naturally” expect. Finally, the interaction of Geometry and Systems Theory can also be fruitful by raising interesting mathematical questions and by leading to results in Geometry, as illustrated by Sussmann 1,2 and 3.
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