Filtered feedback linearization for nonlinear systems with unknown disturbance

Abstract

This paper presents a filtered-feedback-linearization controller for multi-input–multi-output nonlinear systems, where the equilibrium of the zero dynamics is locally asymptotically stable. The controller requires limited model information, specifically, knowledge of the vector relative degree and knowledge of the dynamic-inversion matrix, which is the nonlinear extension of the high-frequency-gain matrix for linear systems. Filtered feedback linearization is a single-parameter high-parameter-stabilizing controller, which is effective for command following and rejection of unknown-and-unmeasured disturbances. This paper analyzes the closed-loop stability and performance, that is, the difference between the actual output and an ideal feedback-linearized closed-loop output. We show that for sufficiently small initial conditions and sufficiently large parameter, the state is bounded, and the L∞ norm of the performance is arbitrarily small.