Abstract
This paper deals with (weakly) regular and abstract bilinear systems which allow some degree of unboundedness in the control and observation operators for infinite-dimensional bilinear systems. By adaption of the notion of abstract linear systems introduced by Salamon (1989) and Weiss (1989a), we give a bilinear version of their approach which works in our setting. The paper investigates also the relation between the shift-invariant bilinear operator and an analytic function. This latter can be considered as a transfer function for bilinear systems. The results thus obtained are used to study the problem of observer design for such systems.
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