High gain observer design for fractional-order non-linear systems with delayed measurements: application to synchronisation of fractional-order chaotic systems

In this study, a high gain observer with delayed driving control signal is designed for synchronisation of fractional-order chaotic systems. The method consists in using two cascade high gain observers in order to compensate for the delay transmission signal from the transmitter to the receiver. For large delay, a fractional-order chain observer composed by high gain cascade delayed observers is proposed. The last observer of this chain estimates the state at the current time while previous observers estimate delayed states. Convergence of the proposed observer is proven. Application to the synchronisation of fractional-order chaotic systems is given. Computer simulations show the effectiveness of the proposed approach.