A new global optimization algorithm for solving Bilinear Matrix Inequalities (BMI) problems is developed. It is based on a dual Lagrange formulation for computing lower bounds that are used in a branching procedure to eliminate partition sets inthe space of non-convex variables. The advantage of the proposed method is twofold. First, lower hound computations reduce to solving easily tractable Linear Matrix Inequality (LMI) problems. Secondly, the lower bounding procedure guarantees globalconvergence of the algorithm when combined with an exhaustive partitioning of the space of non-convex variables. Another important feature is that the branching phase takes place in the space of non-convex variables only, hence limiting the overall costof the algorithm. Also, an important point in the method is that separated LMI constraints are encapsulated into an augmented BMI for improving the lower bound computations. Applications of the algorithm to robust structure/controller design areconsidered.
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