Regular bilinear systems

This paper deals with (weakly) regular and abstract bilinearsystems which allow some degree of unboundedness in the controland observation operators for infinite-dimensional bilinearsystems. By adaption of the notion of abstract linear systemsintroduced by Salamon (1989) and Weiss (1989a), we give a bilinearversion of their approach which works in our setting. The paperinvestigates also the relation between the shift-invariant bilinearoperator and an analytic function. This latter can be consideredas a transfer function for bilinear systems. The results thusobtained are used to study the problem of observer design forsuch systems.