This article treats, in a new framework, a classical design problem, namely H state feedback switched control for discrete time-varying polytopic systems. The main goal is to jointly design a set of state feedback gains and a switching rule in order to assure a pre-specified H guaranteed level. The main contribution is to generalise switched system results to design a switched controller that does not require online measurements of the time-varying parameters. This property has important consequences mainly because the performance quality is preserved even in the lack of parameter information. Our conditions are based on modified RiccatiMetzler inequalities and are described in terms of linear matrix inequalities. An academical example compares the proposed technique with others from the literature.