Summary: 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 one type of gain schedule system, namely, a linear parameter-varying plant scheduling on its exogenous parameters. Conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain schedule design. These conditions confirm and formalize popular notions regarding gain scheduled design, such as the scheduling variable should “vary slowly”.