A semigroup approach to the LQG problem for infinite-dimensional systems

This is a tutorial article on the application of semigroups theory to the linear quadratic Gaussian for linear infinite-dimensional systems. The article is aimed at the nonspecialist in semigroup theory and the results are stated without proofs, but instead are illustrated by two detailed examples; one of a delay model of fluctuating capital stock and the other a distributed model of river pollution.