Adaptation and Disturbance Rejection for Output Synchronization of Incrementally Output-feedback Passive Systems

This note addresses the output synchronization problem of incrementally output-feedback passive nonlinear systems in the presence of exogenous disturbances. Two kinds of distributed controllers are proposed; one placed at the nodes and the other placed at the edges. Each of them is synthesized based on the adaptive control method to cope with the shortage of passivity, and on the internal model principle to deal with the disturbances. The proposed controllers synchronize the outputs of the nonlinear systems when the solution of the closed-loop system is bounded. Based on this, we present a class of systems for which boundedness of the solutions is guaranteed. The analysis used in this note is also applicable to a case where systems are coupled via links modeled by dynamical systems. Simulation results of a network of Van der Pol oscillators show the effectiveness of the proposed methods.