Performance and Calculation of a Limit for the Nonlinear Gain of the Error-Squared Controller

In this paper a performance analysis and two limits for the nonlinear gain of the error-squared controller are presented so that a nonlinear closed-loop system with such controller is asymptotically stable in the Lyapunov sense. The first limit is obtained using Lyapunov stability theorem and the second limit is obtained computing a limit for a linear gain and then the procedure is generalized to the nonlinear case. Simulations had been made comparing the tuning methods in this paper with tuning methods found in the literature and it show that the second limit is more conservative.