For systems affected by time-varying parameters, we provide a novel construction of controllers that lake on-line measurements of these parameters into account to achieve a certain desired performance specification. Since the controller construction is based on multipliers or scalings that are not, as typical in many robust control problems, structured but that are full and do not need to obey any inertia properties, our results permit to reduce the conservatism if allowing for arbitrary fast parameter variations to an arbitrary degree. The paper contains results for parameterized linear matrix inequalities (full block S-procedure) and dualization as well as elimination results for quadratic matrix inequalities that are of independent interest.