Global chaos synchronization and robust filtering in noisy context

In this paper, the problem of global chaos synchronization is addressed. Two propositions borrowed from results of the robust control theory are established to get global synchronization of piecewise-linear dynamical systems in an observer configuration. They are expressed in terms of linear matrix inequalities. One proposition enables the computation of the observer gain matrix which ensures global synchronization with a predetermined transient time called rate of convergence. The second one enables the computation of the observer gain matrix ensuring the minimization of the influence of disturbances in a noisy context leading to a so-called robust filtering. In the same time, propositions give conditions on the structure of the generator to obtain synchronization. Comparisons of performances are pointed out through a numerical example. They clearly highlight the efficiency of robust filtering.