Sequential convex relaxation for robust static output feedback structured control

Reinier Doelman, Michel Verhaegen

Research output: Contribution to journalConference articleScientificpeer-review

3 Citations (Scopus)
115 Downloads (Pure)


We analyse the very general class of uncertain systems that have Linear Fractional Representations (LFRs), and uncertainty blocks in a convex set with a finite number of vertices. For these systems we design static output feedback controllers. In the general case, computing a robust static output feedback controller with optimal performance gives rise to a bilinear matrix inequality (BMI). In this article we show how this BMI problem can be efficiently rewritten to fit in the framework of sequential convex relaxation, a method that searches simultaneously for a feasible controller and one with good performance. As such, our approach does not rely on being supplied with a feasible initial solution to the BMI. This sets it apart from methods that depend on a good initial, feasible starting point to progress from there using an alternating optimization scheme. In addition to using the proposed method, the controller matrices can be of a predetermined fixed structure. Alternatively, an L1 constraint can be easily added to the optimization problem as a convex variant of a cardinality constraint, in order to induce sparsity on the controller matrices.

Original languageEnglish
Pages (from-to)15518-15523
Issue number1
Publication statusPublished - 2017
Event20th World Congress of the International Federation of Automatic Control (IFAC), 2017 - Toulouse, France
Duration: 9 Jul 201714 Jul 2017
Conference number: 20


  • Output feedback control
  • Relaxations
  • Robust control
  • Robust controller synthesis


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