Global optimization in stabilizing controller design

Youngjung Chang, Nikolaos V. Sahinidis

Research output: Contribution to journalArticlepeer-review


In this paper, we develop a global optimization methodology to solve stabilization problems. We first formulate stabilization problems as bilevel programming problems. By invoking the Hurwitz stability conditions, we reformulate these bilevel programs to equivalent single-level nonconvex optimization programs. The branch-and-reduce global optimization algorithm is finally applied to these problems. Using the proposed methodology, we report improved solutions for two feedback stabilization problems from the literature. In addition, we improve the lower bound of the stabilizability parameter of the Belgian chocolate problem from the previous best known 0.96 to 0.973974.

Original languageEnglish (US)
Pages (from-to)509-526
Number of pages18
JournalJournal of Global Optimization
Issue number4
StatePublished - Aug 2007


  • Belgian chocolate problem
  • Global optimization
  • Linear controller design
  • Simultaneous stabilization
  • Stability

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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