Gain-scheduled synthesis with dynamic generalized strictly positive real multipliers: A complete solution

In this paper we provide a solution to the gain-scheduling synthesis problem with possibly unstable dynamic generalized positive real multipliers. This leads to a conclusive resolution of the trouble encountered in two recent papers, in which we either proposed an incomplete solution or one that can be applied for stable multipliers only. This work complements our results on gain-scheduling for dynamic D-scalings with the corresponding complete solution for dynamic D/G-scalings. The merits of D/G-scalings versus D-scalings for parametric uncertainties are well-known. In the present paper we highlight the benefit of unstable dynamic multipliers if compared to the known algorithms for either static or stable dynamic multipliers, respectively.