Robust analysis and synthesis for the nonexistence of periodic solutions in a class of nonlinear systems

This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of the proposed approach.