  The first part of this paper proposed a family of penalized convex
relaxations for solving optimization problems with bilinear matrix inequality
(BMI) constraints. In this part, we generalize our approach to a sequential
scheme which starts from an arbitrary initial point (feasible or infeasible)
and solves a sequence of penalized convex relaxations in order to find feasible
and near-optimal solutions for BMI optimization problems. We evaluate the
performance of the proposed method on the H2 and Hinfinity optimal controller
design problems with both centralized and decentralized structures. The
experimental results based on a variety of benchmark control plants demonstrate
the promising performance of the proposed approach in comparison with the
existing methods.
