A robust control scheme for synchronizing fractional order disturbed chaotic systems with uncertainty and time-varying delay

In this paper, a new method is presented for synchronization between two fractional order delayed chaotic systems, while there is uncertainty on the models and external disturbances enter the systems at the same time. The considered delay in the fractional order system is unspecified and varied with time, and of course it is present in different forms in master and slave systems. External disturbances enter the master–slave systems in a finite manner, albeit with an undetermined upper bound, and uncertainty is present in the nonlinear functions of chaotic systems. The goal of synchronizing a particular class of master–slave chaotic systems is achieved through a combination of adaptive and sliding mode techniques. The sliding mode method has been used to cover the effects of uncertainties and delay functions, and an adaptive method has been applied to ensure the stability of the proposed synchronization technique, disturbance upper bound estimation and overcoming the effects of delay variability. A practical example of the innovative method is simulated in MATLAB environment and the obtained results confirm the optimal efficiency of the proposed synchronization method.