Systematic approach to linear approximation of non-linear stochastic systems Part 1. Asymptotic expansions

Abstract

A new technique is presented for the analysis of non-linear stochastic systems in which they are represented by a series of non-linearly coupled linear systems. Considerable insight is gained in the approximation of non-linear stochastic systems by linear systems and in the use of describing functions. A measure of the error and second-order correction terms for the linear approximation are obtained. The analysis is extended to the non-zero mean case.