Dynamical synchronization control of unidirectionally coupled oscillators: application to antenna arrays

This paper treats the synchronization of a chain of nonlinear and uncertain oscillators. The oscillators are coupled in a unidirectional manner so, the study is reduced to the study of a master-slave configuration. Using the Lyapunov theory of stability, a dynamical controller who guaranties the synchronization is determined. The problem of synchronization is transformed in a problem of asymptotic stabilization for a nonlinear system and then is formulated as a system of linear matrix inequalities where the parameter variations of the two oscillators are modeled by polytopic matrices and the nonlinearity is bounded using the worst case. Using the developed formalism, a dynamical controller who guaranties the synchronization is calculated. The concerned applications are “smart antenna” systems where the carrier signals must be built with the same frequency but independent phases and amplitudes.