期刊
JOURNAL OF GLOBAL OPTIMIZATION
卷 38, 期 4, 页码 509-526出版社
SPRINGER
DOI: 10.1007/s10898-006-9092-2
关键词
stability; simultaneous stabilization; linear controller design; global optimization; Belgian chocolate problem
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.
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