ABSTRACT
It is of great practical as well as theoretical interest to know when, and in what sense, solutions of the abstract equations
x˙(t) = Ax(t) + f(t)
x(0) = x0
(7.1)
exist. Moreover, representations of such solutions in terms of a variation of parameters formula and the semigroup generated by A will play a fundamental role in control and estimation formulations. We begin by summarizing results available in the standard literature on linear semigroups and abstract Cauchy problems.
