Stability and ℋ∞ performance analysis of gain scheduled nonlinear control systems with 𝒟-implementation under slowly varying command inputs

This paper presents some results on the stability and ℋ_∞ performance of nonlinear feedback systems with gain scheduled controller implemented by 𝒟-implementation methodology: (1) For stability, provided the scheduling variable is sufficiently slowly varying and the local linear closed loop systems satisfy a uniform stability constraint, the trajectory of the closed loop nonlinear system remains bounded; and (2) For ℋ_∞ performance, if the local linear controllers are designed to satisfy an ℋ_∞ norm constraint, then the closed loop nonlinear system also satisfies an ℋ_∞ norm inequality. The results use properties of 𝒟-implementation methodology. An example is included to illustrate the ideas