INFINITE-DIMENSIONAL LINEAR-SYSTEMS THEORY

Some control problems for systems described on infinite-dimensional spaces are considered. A mathematical framework in terms of semigroups is developed which enables the generalization of the finite-dimensional results to infinite dimensions, and which includes partial differential equations and delay equations as special cases. After first surveying some finite-dimensional results, abstract dynamical systems are introduced and the systems theory concepts of stability, controllability, observability and the linear quadratic problem are analyzed. The abstract theory is applied to a number of examples.