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The paper proposes a novel iterative output-feedback control design procedure, with necessary and sufficient stability conditions, for linear time-invariant systems within the linear quadratic regulator (LQR) framework. The proposed iterative method has a guaranteed convergence from an initial Lyapunov matrix, obtained for any stabilizing state-feedback gain, to a stabilizing output-feedback solution. Another contribution of the proposed method is that it is computationally much more tractable then algorithms in the literature, since it solves only a Lyapunov equation at each iteration step. Therefore, the proposed algorithm succeed in high dimensional problems where other, state-of-the-art methods fails. Finally, numerical examples illustrate the effectiveness of the proposed method.
Ilka et al. (Sat,) studied this question.