On synchronization of chaotic systems based on the Thau observer design

► We revisit the Thau observer design and consider its application in synchronization with a rigorous analytic method. ► The Thau inequality solution is proposed under one additional assumption. ► The Lorenz–Stenflo system synchronization is examined. ► The hyperchaotic Lorenz system synchronization is examined. In this paper we revisit the Thau observer design and concern its application to the synchronization problem of two Lorenz name related systems in the master–slave formalism. The first one is the Lorenz–Stenflo system possessing a positively invariant ellipsoid while another one is the hyperchaotic Lorenz system possessing a positively invariant cylinder. Information about loci of these invariant domains is applied for the observer design. Further, we present one assertion related to one spectral inequality arisen in the process of assigning stable spectrum to the observer matrix and show its use in the observer design. We demonstrate the efficiency of synchronization schemes for the both of systems with help of numerical simulation.