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The convergence evaluation of the discrete linear quadratic regulator (DLQR) to map the Z-stable plane, is the main target of this research that is oriented to the development of tuning method for multivariable systems. The tuning procedures is based on strategies to select the weighting matrices and dynamic programming. The solutions of DLQR are presented, since Bellman formulations until Riccati and Lyapunov recurrences and are based on the Generalized Policy Iteration, Policy Iteration and Value Iteration. The algorithms and the proposed heuristic method are developed from Riccati and Lyapunov recurrences and are implemented to map the closed loop dynamic eingenvalues in the Z plane. A fourth order model is used to evaluate the convergence and its ability to map the plan Z by selection of the weighting matrices of Optimal Control

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