Abstract
In this paper we take steps towards the development of a robust stabilization theory for nonlinear plants. An approach using the left coprime factorizations of the plant and controller under certain differential boundedness assumptions is used. We first focus attention on a characterization of the class of all stabilizing nonlinear controllers K Q for a nonlinear plant G, parameterized in terms of an arbitrary stable (nonlinear) operator Q. Also, we consider the dual class of all plants G S stabilized by a given nonlinear controller K and parameterized in terms of an arbitrary stable (nonlinear) operator S. We show that a necessary and sufficient condition for K Q to stabilize G S with Q, S not necessarily stable, is that S stabilizes Q. This robust stabilization result is of interest for the solution of problems in the areas of nonlinear adaptive control and simultaneous stabilization. It specializes to known results for linear operators.
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