A note on stability of sliding mode dynamics in suppression of fractional-order chaotic systems

We consider a class of fractional-order chaotic systems which undergoes unknown perturbations. We revisit the problem of sliding mode controller design for robust stabilization of chaotic systems using one control input. In the recent works, it was assumed that one of the system equations are perturbed by uncertainties. For this case we show that the sliding mode dynamics are globally stable which is not addressed so far. Next, we allow that all the system’s equations depend on uncertain terms and provide a theoretical justification for applicability of the existing design. We also determine the least amount of precise information about the chaotic system that is needed to design the controller.