Abstract

This note presents four applications of transversality theory to deriving some topological properties of linear, time-invariant and nonlinear, affine control systems. Special attention is given to the following topics: (i) stratification of linear systems, (ii) generic, one-parameter families of linear systems, (iii) genericity of affine systems having linear controllable approximations, (iv) non-genericity of affine systems equivalent to linear systems. The relevance of the obtained results to the problem of classification of affine systems by state or feedback equivalence is stressed.

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