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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.

MSC:
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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