Robust synchronization of different coupled oscillators: Application to antenna arrays

This paper deals with the synchronization of a chain of nonlinear and uncertain models of nonidentical oscillators. Using Lyapunovʹs theory of stability, a dynamical controller guaranteeing the synchronization of the oscillators is determined. The problem of synchronization is transformed into 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 and their differences are modeled by polytopic matrices. The theoretical result is successfully applied to an array of transistor-based oscillators used in “smart antenna” systems.