Gain scheduling via linear fractional transformations

Abstract

A linear finite-dimensional plant with rational state-space parameter dependence is controlled using a parameter-dependent controller. The parameters are known to take on values in a unit ball, and are known in real time. The goal of control is to stabilize the parameter-dependent closed-loop system, and provide disturbance/error attenuation as measured in induced l2 norms. The approach taken uses the optimally scaled small-gain theorem, and solves the control synthesis problem by reformulating the existence conditions into a finite-dimensional convex optimization. © 1994.