State feedback and estimation of well-posed systems

The class of well-posed systems includes many systems modeled by partial differential equations with boundary control and point sensing as well as many other systems with possibly unbounded control and observation. The closed-loop system created by applying state-feedback to any well-posed system is well-posed. A state-space realization of the closed loop is derived. A similar result holds for state estimation of a well-posed system. Also, the classical state-feedback/estimator structure extends to well-posed systems. In the final section state-space realizations for a doubly coprime factorization for well-posed systems are derived.This research was partially supported by the Fields Institute, which is funded by grants from the Ontario Ministry of Colleges and Universities and the Natural Sciences and Engineering Research Council of Canada, and by a grant from the Natural Sciences and Engineering Research Council of Canada.