In this paper, sufficient conditions of global synchronization in finite-time, which can be a minimum, are presented for the generic class of piecewise linear maps. The conditions of synchronization are based upon general results of the robust control theory, the observability theory, and the specificity of the chaotic motion generated by the map. The robust control theory results enable global synchronization with disturbances cancellation. Observability and assignment of eigenvalues ensure finite-time synchronization. A systematic methodology for designing a global finite-time synchronization derived from those conditions is presented. From a practical point of view, this only requires classical numerical solvers. Finite-time global synchronization can be of interest for applications such as digital communications.
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Millérioux et al. (2001) studied this question.
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