Realization theory of infinite-dimensional linear systems. Part I

This paper deals with the problem of realization of infinitedimensional constant linear continuous-time systems. A framework, suitable for treating this problem, is introduced, including the definitions of input/output maps, systems, weighting patterns, etc. The theorem of the existence and uniqueness of canonical realizations is then proved. Central emphasis is placed on the introduction of a new notion of observability, called topological observability.