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Control design of complex systems offer many challenges, particularly under system uncertainty. System identification, and in particular, parameter estimation is one of the crucial steps for many control strategies requiring a reasonable system model. Then the issue becomes one of selecting the parameter identifier in such a way that convergence can be obtained within a relatively fast period while the control is compensating under uncertainty. In this paper, a convergence rate analysis procedure is developed for multivariable parameter identification. The method allows the designer to select the appropriate initial conditions in order to satisfy a desired convergence rate through an error weighting matrix. Further, this paper develops an exact continuous-time solution in the recursive least squares problem and relates the results to the classical discrete-time case; time-scaling and traditional discrete recursive approaches are shown to be appropriate approximations to this continuous-time result. Finally, the parameter identifier procedure is applied to an example to illustrate the effects of selecting the initial auxiliary matrix to satisfy convergence and the effects of time-scaling on discrete-time and continuous time recursive least squares estimation.