An Approximate Analysis of Transient Response, Moments, and Power Spectrum for Non-linear Feedback Control over the Internet

Hideki SATOH  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.9   pp.2331-2338
Publication Date: 2004/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
linearize,  approximation,  non-linear,  Internet,  MMA,  

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Moment matrix analysis (MMA) that can derive statistical properties of non-linear equations is presented in this paper. First, non-linear stochastic differential, or difference, equations are approximately expressed by simultaneous linear equations of moments defined at discrete events. Next, by eliminating higher order moments, the simultaneous linear equations are reduced to a linear vector equation of their coefficient matrix and a moment vector comprised of the moments of the system state. By computing the eigenvectors and eigenvalues of the coefficient matrix, we can analyze the moments, transient response, and spectrum of the system state. The behavior of Internet traffic was evaluated by using MMA and computer simulation, and it is shown that MMA is effective for evaluating simultaneous non-linear stochastic differential equations.