In this paper, the problem of static output feedback stabilization is considered. By congruence and state-coordinate transformations, a convex condition for static output feedback stabilization is given in terms of a matrix linear inequality while subject to an equality constraint. To facilitate stabilization design via LMI conditions, the equality constraint is satisfied by imposing a structure constraint on matrix variable. Moreover, a numerical construction algorithm and a sufficient condition for the presented convex condition are given as well. Finally, numerical examples demonstrated the utility of the proposed approach for static output feedback stabilization.

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