Approximation of trajectories of non-linear systems by iterates of systems with linear state dynamics

A modification of an iterative Picard process is proposed to approximate the output of a non-linear system by a concatenation of systems with linear state dynamics and non-linear outputs. A local uniform convergence result is given. The motivating example is a non-linear system that arises in surface plasmon resonance experiments to determine protein-protein interaction constants. We show with simulations that for this example the approximants converge not only locally but over the full time interval of interest in the application. (C) 2003 Elsevier B.V. All rights reserved.