A LMI Approach to Tracking Control of Nonlinear Polynomial Systems

Abstract

This paper presents a tracking control approach for a class of nonlinear non-minimum phase systems. This control approach is the combination between an input-output feedback linearization technique and a gain scheduling method to obtain a tracking control structure. The latter is mainly based on the Linear Matrix Inequalities method which allows us to estimate and to enlarge the domain of attraction around operating points. The nonlinear system is represented locally by variation polynomial models. The polynomial models are then used to design a family of feedback controllers. We propose a nonlinear gain scheduling procedure for the problem of guaranteed transition from an actual operating point to a desired one along the reference trajectory. The theoretical results are applied to a non-minimum phase continuously stirred tank reactor in order to illustrate the effectiveness of the proposed approach