On the nonexistence of limit cycles for a class of nonlinear systems under parameter uncertainties

This paper concerns the nonexistence of limit cycles in a class of nonlinear systems which are subject to norm-bounded parameter uncertainty in the state and input matrices. Based on Kalman-Yakubovich-Popov (KYP) lemma, sufficient conditions for the nonexistence of limit cycles in such uncertain nonlinear systems are derived in terms of linear matrix inequalities (LMIs) and an efficient way for estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. Based on the results, static state feedback controller and dynamic output feedback controller are designed ensuring the closed-loop uncertain nonlinear system has no limit cycles respectively. A concrete application to Chua´s circuit shows the applicability of the proposed approach.