D.C. Optimization Approach to Robust Control: Feasibility Problems

The feasibility problem for constant scaling in output feedback control is considered. This is an inherently di cult problem [20, 21] since the set of feasible solutions is nonconvex and may be disconnected. Nevertheless, we show that this problem can be reduced to the global maximization of a concave function over a convex set, or alternatively, to the global minimization of a convex program with an additional reverse convex constraint. Thus this feasiblity problem belongs to the realm of d.c. optimization [14, 15, 32, 33], a new eld which has recently emerged as an active promising research direction in nonconvex global optimization. By exploiting the speci c d.c. structure of the problem, several algorithms are proposed which at every iteration require solving only either convex or linear subproblems. Analogous algorithms with new characterizations are proposed for the Bilinear Matrix Inequality (BMI) feasibility problem.