Extensions of linear systems to duals of countably Hilbertian spaces with graph topology
WU Jingbo, Shangwei Zhu · IMA Journal of Mathematical Control and Information · 1993
The state space for an infinite-dimensional system of the form ⊙ = Ax + Bu can be extended to the dual of a countably Hilbertain space with graph toplogy. The Study of countably Hilbertian spaces with graph topology and their duals is made. The structures of the extensions of a C 0 semigroup and the stability theory of the restrictions and extensions of the semigroup are illustrated. An existence and uniqueness theorem of the solution of the extended system is given.