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D. c. optimization approach to robust control: Feasibility problems. (English) Zbl 0998.93012
Global optimization algorithms are designed to solve numerically some difficult non-convex problems arising in robust control of linear systems, namely \(H_\infty\) output feedback control with constant scalings and more general bilinear matrix inequality problems. It is shown how the particular problem structure can be exploited in a branch and bound scheme: branching is performed on a reduced number of variables, whereas bounding is done on d.c. (difference of convex functions) inequalities relaxed to linear or linear matrix constraints. Very preliminary numerical results are described.

93B40 Computational methods in systems theory (MSC2010)
90C26 Nonconvex programming, global optimization
93B36 \(H^\infty\)-control
90C22 Semidefinite programming
93D09 Robust stability
93B51 Design techniques (robust design, computer-aided design, etc.)
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