Robust gain-scheduled controller synthesis is convex for systems without control channel uncertainties

In this paper we generalize our previous results on robust controller synthesis to robust gain-scheduled controller synthesis. We present novel insights that reveal how the robust gain-scheduled controller synthesis problem can be turned into a semi-definite program, under the hypothesis that (i) the control channel is not affected by uncertainties and (ii) the uncertainties and scheduling variables are described by full-block multipliers. Feasibility of the resulting LMI conditions ensures the existence of gain-scheduled controllers that guarantee robust stability and performance for the corresponding closed-loop uncertain system.