Abstract
Abstract Linearly approximating the nonlinear system so as to analyse it and design a control law, and then applying this control law to the original system has been a fairly common practice. The swing-out, as a measure of nonlinearity of a dynamical system, is incorporated in understanding the relationship between the small-time reachable sets of the nonlinear control system and its linear approximation in the plane. Linear approximation about nonequilibrium points are considered. Further facts are derived for a good linear approximation. Behaviour of the real system under a bang-bang control law particularly designed using the linear approximation of the system is examined.
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