Extended circle criterion for determination of gain and phase margins of Lur’e systems

Abstract The main goal of the present work is proposing a new approach to determine stability margins for a class of nonlinear systems. In particular, we propose a new approach to find the gain and phase margins of Lur’e type nonlinear systems with higher accuracy. To do so, we use multi-section extended circle criterion which is based on Lyapunov stability theorem. To find more precise values of the stability margins, an optimization problem is defined and solved using a nonlinear estimator. Two examples are provided to evaluate the effectiveness of the proposed approach and compare the results to those of the existing methods.