Practical implementation of adaptive impulsive observer based chaotic synchronization scheme

This paper proposes an adaptive impulsive observer, suitable for impulsive chaos synchronization schemes. Only by using the output of the drive system at discrete instant times, the observer would be able to estimate both states and unknown parameters of the uncertain drive system. The stability of the observer is proved through a theorem which gives an upper bound on the maximum possible impulses distance. More importantly, the proposed observer does not require the observability condition on the linear part of the system while most traditional observers require that condition. The observer is then implemented practically by electrical circuits to synchronize with an uncertain chaotic Lorenz system. Presented practical and numerical simulation results show the effectiveness of the proposed observer even when the coupling signal is scalar.