Synchronization preservation under linear polynomial modifications

Robustness and preservation of stability and synchronization in the presence of structural changes is an important issue in the study of chaotic dynamical systems. In this work we present a methodology to establish conditions for preservation of stability in dynamical system in terms of linear matrix polynomial evaluation. The idea is to construct a group of dynamical transformations under which stability is retained along the stable, unstable and synchronization manifolds using simultaneous Schur decompositions.