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This paper presents the computation of two limits for the nonlinear gain of the error-squared controller considering two procedures and performance analysis so that a closed-loop system with this control algorithm is asymptotically stable in the Lyapunov sense. The first limit for the nonlinear gain is obtained using Lyapunov stability theorem. The second limit for the nonlinear gain is obtained computing a limit for a linear gain and then the procedure is generalized to the nonlinear case. Simulation results were made comparing the tuning methods proposed in this paper, for the error-squared controller, with other tuning conventional methods found in the literature. It shown that the limit computed from second method is more conservative.

<b>The error-squared controller: a proposed for computation of nonlinear gain through Lyapunov stability analysis