Abstract
We introduce the notion of uniform system approximation and use it to solve the following problem: Given a single input nonlinear system (f, g): x ̇ = f(x) + g(x)u that is linearly controllable on a manifold E of equilibrium points, find vector fields f, g such that (f, g) and f, g agree to first order on E and ( f, g) is input-to-state linearizable on a neighborhood of E . The solution proceeds by constructing a linearizable uniform system approximation and yields, as a by product, a feedback control law that can be used to guarantee stable operation of the given system in a neighborhood of E . This includes, for example, smooth transitions between operating points that are not necessarily close to each other. A simple example is given to illustrate the approach.
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