This project is directed towards the study of infinite dimensional balanced realizations, both from the point of view of improving the basic understanding of these realizations and of providing further tools for model reductions of infinite dimensional systems. The project will focus on the specific questions of asymptotic and exponential stability of the balanced systems and the boundedness properties of the system operators. A further important point which will be addressed is the issue of whether general Trotter-Kato type convergence results can be proved for the balanced approximation scheme. Many engineering systems, such as highly flexible mechanical systems, inherently contain infinitely many degrees of freedom and therefore any accurate mathematical description of such a system must necessarily be infinite dimensional. There are several ways to achieve such a mathematical description. One recent approach is based on models of finite complexity. This method of "balanced realizations" has proved very successful in practice.
