Robust stabilization of nonlinear plants via left coprime factorizations

The authors describe steps toward 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. Attention is focused 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 considered is 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. It is shown 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