In this paper, we propose new LMI-based conditions to design output-feedback controllers under structural constraints. The conditions are given in terms of LMI's with rank constraints and we solve them by means of the alternating projection algorithm. Even though the algorithm does not ensure global convergence, extensive numerical experiments demonstrate that the proposed design method is promising in designing structured and/or multiobjective controllers, provided that the dimension of the closed-loop systems is not excessively large.
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