On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters

This paper presents the robust stabilization problem of linear and non-linear fractional-order systems with non-linear uncertain parameters. The uncertainty in the model appears in the form of the combination of ‘additive perturbation’ and ‘multiplicative perturbation’. Sufficient conditions for the robust asymptotical stabilization of linear fractional-order systems are presented in terms of linear matrix inequalities (LMIs) with the fractional-order 0<α<1. Sufficient conditions for the robust asymptotical stabilization of non-linear fractional-order systems are then derived using a generalization of the Gronwall–Bellman approach. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.