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

Christian A. Rösinger, Carsten W. Scherer

Abstract

We focus on the $\mathcal{H}_2$-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 finiteness of the $\mathcal{H}_2$-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.

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

Abstract

We focus on the -gain-scheduling synthesis problem for time-varying parametric scheduling blocks with scalings. Recently, we have presented a solution of this problem for - and positive real scalings by guaranteeing finiteness of the -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.

Paper Structure

This paper contains 3 sections, 3 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Structured plant and controller representations

Figures (1)

  • Figure 1: Feedback-loop for gain-scheduling.