Аннотация:The problem of synthesis of an asymptotic observer for a linear system with l outputs y(t)=Cx(t) and m unknown inputs is considered. The inputs act through the matrix D. The case of a hyper-output system, i.e. l>m, is considered. For such systems, methods for constructing observers are well developed if the CD matrix of the transition from input to output has a full rank. In this paper we investigate the case when $rank(CD)