Sufficient stability conditions of fractional systems with perturbed differentiation orders

Abstract

© 2017 In this paper sufficient stability conditions are established for fractional systems with perturbed differentiation orders. It is an extension of the recently published paper Rapaic and Malti [2016] which allows henceforth increasing the highest differentiation order. The maximum allowable variation on all differentiation orders is computed so that the stability (respectively instability) is preserved when differentiation orders are perturbed away from the commensurate ones. The maximum allowable variations are compared in both cases: when the highest order is allowed to be increased and when it is not. The established conditions allow concluding on the stability of incommensurate fractional systems on the basis of Matignon's theorem and the additional sufficient condition.