Dynamical synchronization for coupled oscillators: application to antenna arrays

This paper treats the synchronization of two identical nonlinear oscillators. Using the Lyapunov theory of stability and the matrix separation lemma, a dynamical controller is determined. The problem is formulated as a system of linear matrix inequalities where the nonlinearity is bounded using the worst case. The concerned applications are "smart antenna" systems where the carrier signals must be built with the same frequency but independent phases and amplitudes