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

In this paper we continue our efforts to arrive at a solution of the gain-scheduling controller design problem with dynamic multipliers. Although a solution for D-scalings is available, this scenario leads to conservatism if scheduling on real parameters. This motivates to consider the very same problem with D/G-scalings, for which we recently proposed a design framework with generalized positive real multipliers. The present paper closes a gap in this previous approach and provides necessary and sufficient convex conditions for the existence of gain-scheduling controllers if the multipliers are stable and positive real. Examples illustrate the possibility for a substantial reduction of conservatism with the novel solution.