This technical note deals with the switched supervised control of linear parameter varying systems whose parameters values are online acquirable only with an arbitrarily large degree of uncertainty. The purpose is to define a switching policy inside a family of predesigned controllers so that the switched closed-loop system result to be exponentially stable. The proposed switching logic is based on a performance-evaluation criterion which uses a measurable Lyapunov-like functional of the output. The exponential stability condition is derived imposing a sufficient long time interval over which the functional is decreasing. An interesting feature of the technical note is that no particular structure on the kind of uncertainty affecting the parameter values is assumed.