MINES ParisTech CAS - Centre automatique et systèmes

NECESSARY AND SUFFICIENT CONDITION FOR EXPONENTIAL SYNCHRONIZATION OF NONLINEAR SYSTEMS

Séance du jeudi 16 février 2016, Salle L106, 14h00-16h00.
14h00 : Vincent Andrieu, LAGEP, Univ. de Lyon, CNRS
Based on recent works on transverse exponential stability, some necessary and sufficient conditions for the existence of a (locally) exponential synchronizer are established. We show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems (on the synchronization manifold) by a linear state feedback. This, in turns, is also equivalent to the existence of a symmetric covariant tensor field which satisfies a kind of Lyapunov inequality. Based on this property, we provide the construction of such synchronizer. We discuss then the possibility to achieve global synchronization.