For many practical applications, it is necessary to design controllers that are, one the one hand, robust against bounded uncertainty in selected parameters and external disturbances. On the other hand, it is also quite common for such systems, that state constraints need to be accounted for which must not be exceeded for any possible parameter value. Although the task is quite challenging, several robust control design procedures were designed in recent years which allow for solving these problems, especially with respect to the latter aspect. In this paper, such robust control procedures are combined in a novel manner with an interval observer to additionally handle the influence of unknown but bounded measurement noise and to prevent the violation of state constraints in a provable fashion.