Current state of system approximation for deterministic and stochastic systems

This paper is concerned with the current state of the field of system approximation for physical and abstract systems. Under certain conditions a system may be regarded as a mathematical operator G:U/spl rarr/V mapping excitations u(t) in U into responses v(t)=(Gu)(t) in V. Intuitively then, a system approximation is a second system G/spl circ/:S/spl rarr/V mapping excitations u(t) in a subset S of U into responses v/spl circ/(t)=(G/spl circ/u)(t) in such a manner that v/spl circ/(t) is similar to v(t) in a useful sense. Defined this way, G/spl circ/ provides an approximate representation of the behavior of G. The concept of system approximation is discussed, the elements of the approximation problem described, and the current state of system approximation methods discussed.