On Synthesis of Practically Valid Gain-Scheduled Controllers, Report no. 2528

Sufficient conditions for the existence of a gain scheduled controller for LPV systems is presented. It is shown that it is always possible to find a controller that depends on the parameters but which is independent of the rate of parameter variation. The conditions are three LMIs, which are similar to the conditions used for standard H∞ synthesis problems. In the general case, the controller needs to have twice as many states as the original system. If a lower-order controllers is searched for, a rateindependent controller still resists a convex formulation.