Adaptive Pinning Control of Networks of Circuits and Systems in Lur´e Form

This paper is concerned with the derivation of a distributed adaptive control strategy for synchronization and consensus of networks of nonlinear systems in the Lur´e form. In particular, time-varying feedback coupling and control gains are considered, whose derivatives are functions of local error over each edge in the network. The strategy is shown to be successful in controlling the network to the desired trajectory. The stability analysis also encompasses the case of a generic inner coupling matrix, where the coupling may not involve all state variables. A set of simple sufficient conditions is derived that can also be used to design the inner coupling configuration. The theoretical derivation is complemented by its validation on a set of representative examples.