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arXiv · 1109.3320

Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with application to Static Output Feedback

Quoc Tran Dinh·Suat Gumussoy·Wim Michiels·Moritz Diehl
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Abstract

A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to various output feedback controller synthesis problems are presented. In these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from COMPleib library.

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Quoc Tran Dinh, Suat Gumussoy, Wim Michiels, Moritz Diehl. 2011-09-15. Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with application to Static Output Feedback. https://arxiv.org/abs/1109.3320

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