Gain-scheduled synthesis with dynamic positive real multipliers

If designing robust controllers based on multiplier or separation techniques, one is confronted with weighting filters that are not necessarily stable. For optimal synthesis, this requires controllers to be only partially internally stabilizing. In this paper we propose a new synthesis framework for possibly unstable performance weights. It is further shown how these results can be used to design gain-scheduling controllers with dynamic positive real multipliers by convex optimization, a problem without any analogous solution in the literature.