Robust D-stability with mixed-type uncertainties

In this note, we deal with the robust D-stability analysis for systems with both structured and unstructured uncertainties. First, an extension of the small gain theorem is presented for robust D-stability analysis of systems with mixed-type uncertainties. Second, an edge verification result is obtained when the structured uncertainty is described by an interval plant. Finally, for some special root location regions, this problem has been converted to the computation problem of the maximal H_∞ norm of a transfer function with parametric uncertainties and some explicit vertex results are obtained. It can be seen that the computation complexity is significantly reduced in these special cases.