Feedback synchronization using pole-placement control (Q2708542)

The authors present a feedback method for the synchronization of two chaotic systems. The feedback design is based on the classical pole placement method for the linearized system, where the feedback is chosen in such a way that the resulting closed loop system's matrix becomes asymptotically stable. NEWLINENEWLINENEWLINEIn the application to synchronization, the linearization has to be carried out along the trajectories of the driving system, which results in a time-varying linear system. As the authors themselves note, it is well known that asymptotic stability of the resulting frozen closed loop matrices is not sufficient for asymptotic stability of the time varying system, but they claim (without reasoning) that for the specific synchronization problem it is sufficient. NEWLINENEWLINENEWLINEIn any case, the numerical experiments with the Hénon and the double rotor maps show good results.