This paper is concerned with the synthesis of static output feedback (SOF) control satisfying multi-objective H2/H performance for LTI systems. Given an initially stabilizing SOF gain Ko, an estimate of the set of stabilizing gains is obtained using Monte Carlo based randomized search. A synthesis algorithm which combines both linear matrix inequalities (LMIs) and genetic algorithms (GA) is proposed. To improve the efficiency of this hybrid algorithm, the GA employs a projection-like operation so that the solution candidates lie in the interior of the set of stabilizing gains in a neighborhood of Ko.

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