A Structure Exploiting SDP Solver for Robust Controller Synthesis

IEEE Control Systems Letters, vol. 7, pp. 1831–1836

Abstract

In this paper, we revisit structure exploiting SDP solvers dedicated to the solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These SDPs inherit their name from the KYP lemma and they play a crucial role in e.g. robustness analysis, robust state feedback synthesis, and robust estimator synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require O(n6) arithmetic operations per Newton step to solve this class of problems, where n is the state dimension of the dynamical system under consideration. Specialized solvers reduce this complexity to O(n3). However, existing specialized solvers do not include semi-definite constraints on the Lyapunov matrix, which is necessary for controller synthesis. In this paper, we show how to include such constraints in structure exploiting KYP-SDP solvers.

Authors 4

1. Dennis Gramlich Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Chair of Intelligent Control Systems, RWTH Aachen University, Aachen, Germany

2. Tobias Holicki

   University of Stuttgart

   Affiliation as printed

   Chair of Mathematical Systems Theory, University of Stuttgart, Stuttgart, Germany

3. Carsten W. Scherer

   University of Stuttgart

   Affiliation as printed

   Chair of Mathematical Systems Theory, University of Stuttgart, Stuttgart, Germany

4. Christian Ebenbauer Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Chair of Intelligent Control Systems, RWTH Aachen University, Aachen, Germany