Nonlinear control by input-output pole assignment: state space derivation

Abstract

This paper considers pole assignment control of nonlinear dynamic systems described by State Dependent Parameter (SDP) models. The approach follows from earlier research into linear Non-Minimal State Space (NMSS) methods but, in the nonlinear case, the control gains are updated at each sampling instant. The algorithm is derived directly from the NMSS model, necessitating the introduction of a state dependent transformation matrix. This state variable feedback derivation lends itself to straightforward controllability and stability analysis. In this regard, the paper shows that the closed-loop system reduces to a linear transfer function with the specified poles; and that these differ from the closed-loop transition matrix eigenvalues.