Differential State Space Descriptions of Nonlinear Time Variant Hereditary Differential Systems

Abstract

This paper investigates the problem which trajectories of a system ∑ defined by a nonlinear functional differential equation in a real Banach space E, may be described by an operator differential equation in appropriate state spaces. The use of semi-group methods is avoided by a separate analayis of the differential equation ż = Az, where A is the first order differential operator on the state space. Necessary and sufficient conditions for the segment function to be absolutely continuous are derived, The sets of admissible initial data are determined. The equivalence of the functional differential equation with the operator differential equation in the state space (ϐ and MP spaces) is established for these initial data.