Gain scheduling dynamic linear controllers for a nonlinear plant

For a general type of nonlinear tracking problem, we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points. A necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented. Using this condition, the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed, and ad hoc approaches to scheduling can be analyzed.