Distributionally Robust LMI Synthesis for LTI Systems

IEEE Transactions on Automatic Control, pp. 1–14

Abstract

This article shows that distributionally robust controller synthesis as investigated in \cite{taskesen2024distributionally} can be formulated as a convex linear matrix inequality (LMI) synthesis problem. To this end, we rely on well-established convexification techniques from robust control. The LMI synthesis problem we propose has the advantage that it can be solved efficiently using off-the-shelf semi-definite programming (SDP) solvers. In addition, our formulation exposes the studied distributionally robust controller synthesis problem as an instance of robust $H_2$ synthesis.

Authors 4

1. Dennis Gramlich Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Shuhao Yan

   University of Stuttgart

   Affiliation as printed

   University of Stuttgart

3. Carsten W. Scherer

   University of Stuttgart

   Affiliation as printed

   University of Stuttgart

4. Christian Ebenbauer Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University