Due to the appearance of uncontrollable events in discrete-event systems, one may wish to replace the behavior leading to the uncontrollability of pre-specified language by some quite similar one. To capture this similarity, we introduce metric to traditional supervisory control theory and generalize the concept of original controllability to lambda-controllability, where lambda indicates the similarity degree of two languages. A necessary and sufficient condition for a language to be lambda-controllable is provided. We then examine some properties of lambda-controllable languages and present an approach to optimizing a realization.