Robust asymptotical stability of fractional-order linear systems with structured perturbations

This paper considers the robust asymptotical stability problem of fractional-order linear systems with structured perturbations, which are more general than the investigated fractional-order interval systems. Based on the Kronecker product and μμ-analysis, necessary and sufficient conditions for the robust asymptotical stability are established by transforming such a problem into checking the nonsingularity of a class of uncertain matrices. Furthermore, the robustness bounds with respect to parametric perturbations to preserve the asymptotical stability are given in terms of the structured singular values. Finally, illustrative examples are given to show the effectiveness of the proposed approach.