On the application of alternating projection under the constraint of linear matrix inequalities

In this paper, alternating projection under the constraint of linear matrix inequalities (LMIs) is investigated to solve the following two problems: finding the intersection of several convex LMI sets and designing an output-feedback stabilizing controller. Each problem is formulated as a quadratic optimization problem under LMI constraints. A numerical algorithm based on the concept of alternating projection is proposed. The algorithm is demonstrated using a vertical-strip pole-assignment example.