Gain-Scheduling Control With Dynamic Multipliers by Convex Optimization

In this paper we provide a solution to the gain-scheduling synthesis problem (GSP) for structured parametric and dynamic passive uncertainties, which encompasses an approach for norm-bounded uncertainties as considered in classical structured singular value theory. If compared to known approaches, the distinguishing feature is the use of frequency-dependent multipliers to guarantee stability and performance of the controlled system. On the basis of suitable parameterizations of these multipliers, we develop necessary and sufficient conditions for the existence of gain-scheduling controllers and discuss the benefits of this new design methodology.