Robust stability criterion for fractional-order systems with interval uncertain coefficients and a time-delay

•Robust stability of interval fractional-order systems with a time-delay is studied.•A method is offered to avoid the calculations for the redundant vertices.•The position relationship between the origin and the value set is described.•Based on the zero exclusion principle, the robust stability criterion is proposed.

This study investigates the robust stability of fractional-order systems with interval coefficients and a time-delay. By the Minkowski Sum, the vertices of value set with respect to the characteristic function of the investigated fractional-order system are offered, avoiding the calculations of the redundant vertices. Meanwhile, a function depending on the obtained vertices is defined to represent the position relationship between the origin and the value set. Based on the zero exclusion principle, we propose sufficient and necessary conditions to determine the robust stability of fractional-order systems with interval uncertain coefficients and a time-delay. Finally, illustrative examples are offered to verify the effectiveness of the proposed robust stability criterion.