Robust observer-based synchronisation of chaotic oscillators with structural perturbations and input nonlinearity

This paper presents a generalised robust adaptive chaotic synchronisation method for chaotic systems with structural perturbations. One control input is used to synchronise both systems exponentially fast based on Lyapunov theory. This approach cannot only make the outputs of both master and slave systems reach synchronisation with the passage of time between both systems but it can also reduce the effect of external perturbations and input nonlinearities. By assuming bounded solutions of the nominal uncoupled systems, sufficient conditions have been derived for boundedness of the solutions of two different classes of chaotic systems with input nonlinearity affected by structural perturbations. The propose approach offers a systematic design procedure for robust adaptive synchronisation of a large class of chaotic systems in the chaos research literature. As an illustration of the effectiveness and robustness of the proposed strategy, synchronisation problem of a master system consists of a perturbed modified Colpitts oscillator and an observer consisting of a Chua oscillator. It was found that the controller maintains robust stable synchronisation in the presence of exoteric perturbations and structural uncertainties.