Necessary and sufficient condition for local exponential synchronization of nonlinear systems

Abstract : 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.
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Vincent Andrieu, Bayu Jayawardhana, Sophie Tarbouriech. Necessary and sufficient condition for local exponential synchronization of nonlinear systems. 54th IEEE Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. pp.2981 - 2986, ⟨10.1109/CDC.2015.7402586⟩. ⟨hal-01856301⟩

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