In this paper, a new algorithm is proposed for the design of a family of controllers to be used within an adaptive switching control scheme. The resulting switching controller is able to attenuate the effects of disturbances having uncertain and possibly time-varying characteristics, as well as to ensure stability under arbitrary switching sequences. Specifically, the stability requirement is addressed within the synthesis of the set of controllers by imposing some constraints in LMI form. The overall synthesis algorithm is formulated in terms of convex optimization problems, which can be solved by means of standard tools. The validity of the proposed solution is underlined by showing simulation results on an adaptive optics case study.