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Some Results on Exponential Synchronization of Nonlinear Systems

Abstract : Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. 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 turn, is also equivalent to the existence of a symmetric covariant tensor field, which satisfies a Control Matrix Function inequality. Based on this result, we provide the construction of such synchronizer via backstepping approaches. In some particular cases, we show how global exponential synchronization may be obtained.
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Contributor : Vincent Andrieu Connect in order to contact the contributor
Submitted on : Thursday, January 25, 2018 - 10:02:56 AM
Last modification on : Tuesday, October 25, 2022 - 11:58:11 AM
Long-term archiving on: : Thursday, May 24, 2018 - 8:10:57 PM


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Vincent Andrieu, Bayu Jayawardhana, Sophie Tarbouriech. Some Results on Exponential Synchronization of Nonlinear Systems. IEEE Transactions on Automatic Control, 2018, 63 (4), pp.1213-1219. ⟨10.1109/TAC.2017.2789244⟩. ⟨hal-01324150v4⟩



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