Output synchronization of Lur´e-type nonlinear systems in the presence of input disturbances

This paper deals with the output synchronization problem of a network of Lur´e-type nonlinear systems under exogenous disturbances that are different from node to node and introduce a source of heterogeneity in the network. The Lur´e-type nonlinear systems we consider possess the properties of incremental output-feedback passivity and input-to-state stability relative to a set. Based on these properties, we propose a distributed controller which is a combination of adaptive laws to cope with the shortage of passivity and internal models to attenuate the net effect of disturbances on synchronization error. By the input-to-state stability of the Lur´e-type systems, the proposed controller guarantees boundedness of the closed-loop solutions and synchronization of the outputs of the nonlinear systems. Finally, a computer simulation of a network of Chua´s circuits is given to demonstrate the validity of the proposed result.