Well-posedness and accuracy of harmonic linearization for Lur’e systems

In this paper we deal with the performance analysis of harmonically forced nonlinear systems of Lur´e type. We use harmonic linearization to obtain a linear approximation of the nonlinear system, and provide a frequency domain condition that guarantees a unique positive real solution to the harmonic balance equation for a certain class of nonlinearities. Furthermore, we provide an estimate on the error between the solutions of the nonlinear system and its linear approximation. Finally, we give an example to illustrate the presented theory.