This work deals with the spectral factorization problem for distributed parameter systems, especially the method of spectral factorization by symmetric extraction. This problem has been the heart of many studies recently, and plays a central role in solving control problems associated with infinite-dimensional linear systems, including the linear-quadratic optimal control problem.
This work focuses on the study of an operator belonging to the class of Sturm-Liouville operators that are densely defined in the Lebesgue space of square-integrable functions. This particular operator is used in the modelling of biochemical tubular reactors with axial dispersion.
The main result of this work states that the method of spectral factorization by symmetric extraction is convergent for a class of distributed parameter systems which is based on this operator. This result involves several results linking the theories of semigroup state-space systems, Sturm-Liouville systems and Riesz-spectral systems.