Lifting to Passivity for H2-Gain-Scheduling Synthesis with Full Block Scalings

Abstract

We focus on the H2-gain-scheduling synthesis problem for time-varying parametric scheduling blocks with scalings. Recently, we have presented a solution of this problem for D- and positive real scalings by guaranteeing fmiteness of the H2-norm for the closed-loop system with suitable linear fractional plant and controller representations. In order to reduce conservatism, we extend these methods to full block scalings by designing a triangular scheduling function and by introducing a new lifting technique for gain-scheduled synthesis that enables convexification.