{
  "id": "2001.05740",
  "version": "v1",
  "published": "2020-01-16T11:19:37.000Z",
  "updated": "2020-01-16T11:19:37.000Z",
  "title": "Lifting to Passivity for $\\mathcal{H}_2$-Gain-Scheduling Synthesis with Full Block Scalings",
  "authors": [
    "Christian A. Rösinger",
    "Carsten W. Scherer"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-16T11:19:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full block scalings",
      "suitable linear fractional plant",
      "time-varying parametric scheduling blocks",
      "enables convexification",
      "positive real scalings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}