Some conditions which make the constantly scaled H∞ control synthesis problems convex

We present some conditions which make the linear fractional transformation constantly scaled H_∞ control synthesis problems convex. Moreover, we show that a class of reduced order controller synthesis with scalings can be reduced to convex problems, as long as some of state variables are exactly available. If one of the conditions proposed in the paper holds, the constantly scaled H_∞ control synthesis problems can be solved efficiently as LMI problems. The results presented include as special cases the existing results such as the state feedback and the full information problems