# zbMATH — the first resource for mathematics

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.)
Full Text: