Dynamic controller design for synchronization of Lur’e type systems subject to control saturation

Abstract

Abstract This paper addresses the synchronization problem between two nonlinear Lur’e systems subject to control saturation. Assuming that only the output of master and slave systems are measurable, the design of a nonlinear dynamic feedback controller is considered. Based on Lyapunov arguments and a sector-based approach to deal with the system nonlinearities, linear matrices inequalities (LMI) to ensure the local asymptotic convergence of the slave state to the master one (i.e. to ensure null synchronization error) are derived. The design of the controller parameters is then carried out by the solution of a convex optimization problem aiming to maximize a set of initial conditions for which the synchronization is guaranteed. A numerical example considering the synchronization of a Chua’s circuit illustrates the proposed method.