The objective of this project is to conduct research concerning the qualitative properties of nonlinear systems, with emphasis on the theory of representations. The research proposed concerns in part an interesting new type of representation that is an extension of the familiar impulse-response representation for linear systems. Applications involving, for example, stability theory and systems governed by nonlinear differential equations are considered. Related nonlinear-system research concerning representations, stability, iteration and convergence, etc., is also pursued and this would bear on, for example, nonlinear filtering for image processing. The tools to be used include topology, functional analysis, and integration theory.
