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In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than or equal $\frac{1}{2}$ when all unimodular eigenvalues of the closed-loop matrix are semi-simple. Numerical examples are shown to illustrate the feasibility and efficiency of the proposed algorithm.

STRUCTURED DOUBLING ALGORITHM FOR DISCRETE-TIME ALGEBRAIC RICCATI EQUATIONS WITH SINGULAR CONTROL WEIGHTING MATRICES