LMI conditions for contraction and synchronization ?

摘要

This paper deals with a systematic way to check if a certain class of nonlinear systems can define a contraction. The proposed approach combines the use of sector bound condition or monotonic condition satisfied by the nonlinearities with the use of an adequate control function matrix. The contraction analysis results are provided under the form of linear matrix inequalities (LMIs). The design of a nonlinear control law (that is a control law depending on nonlinearities) is proposed in order for the closed loop to be a contraction. The adaptation of the contraction results to the synchronization of n identical nonlinear systems is also investigated by considering two kinds of communication graphs (full and general undirected ones).