Analysis of Gain Scheduled Control for Nonlinear Plants

Gain scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees on the robustness, performance, or even nominal stability of the overall gain scheduled design. This paper presents such an analysis for two types of nonlinear gain scheduled control systems: 1) scheduling on a reference trajectory; and 2) scheduling on the plant output. Conditions are given which guarantee stability, robustness, and performance properties of the global gain scheduled designs. These conditions confirm and formalize popular notions regarding gain scheduled designs, such as the scheduling variable should “vary slowly” and “capture the plant's nonlinearities.” These results extend previous work by the authors which addressed the case of linear plants whose dynamics depend on exogenous parameters.