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In this article, models and a genetic algorithm convergence analysis method for the LQR weight matrices determination are presented. The control goal is the eigenstructures allocation in multivariable dynamic systems imposed by the optimal control law, and the analysis procedure goal is the speeding up of the convergence through metrics based upon first and second order statistical momentum. The proposal performance is evaluated under the initial populations building point of view and the populations search process, whereas the convergence analysis leads to the development of rules based upon fitness function metrics. Tests for the genetic search models performance evaluation and for the control law efficiency are conducted with a 6th order dynamic model representing an aircraft.