Using linear approximations of nonlinear systems has long been a practice to design control laws. In this paper, an analysis is given involving linear approximation of the Inonlinear control system and small-time reachable sets in M2. A useful concept, the swing-out, which is a measure of nonlinearity, is defined. This is used to examine the relationship between the small-time reachable sets of the nonlinear control system and its linear approximation. Behaviour of the nonlinear system under a control law is examined within this context. More facts are given about the swing-out for some special cases.
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