Lifting to Passivity for $\mathcal{H}_2$-Gain-Scheduling Synthesis with Full Block Scalings

Christian A. Rösinger, Carsten W. Scherer

Published 2020-01-16Version 1

We focus on the $\mathcal{H}_2$-gain-scheduling synthesis problem for time-varying parametric scheduling blocks with full block scalings. Recently, we have presented a solution of this problem for $D$- and positive real scalings by relying on a convexifying transformation for the controller parameters and by guaranteeing finiteness of the $\mathcal{H}_2$-norm for the closed-loop system with suitable linear fractional plant and controller representations. 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.