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Combining Convex–Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback

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4 Author(s)
Quoc Tran Dinh ; Fac. of Math.-Mech.-Inf., Hanoi Univ. of Sci., Hanoi, Vietnam ; Gumussoy, S. ; Michiels, W. ; Diehl, M.

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 the COMPleib library.

Published in:

Automatic Control, IEEE Transactions on  (Volume:57 ,  Issue: 6 )