Synchronization for a class of nondifferentially flat chaotic systems by means of a PI Observer

In this paper a proportional integral reduced order observer (PIO) for the synchronization problem of a class of nondifferentially flat chaotic systems is proposed. In order to take advantage of the system characteristics, differential polynomials are used for the observer design. The asymptotic stability proof for the resulting estimation error is given. The effectiveness of the methodology proposed here is exemplified by designing a PIO for a Lorenz attractor and doing the respective numerical simulation. The results obtained by the PIO are contrasted with those acquired by a proportional observer (PO) whose design is based in the same methodology, this in order to show the improvement given by an integral action.