This monograph deals with approximation and noise cancellation of
dynamical systems which include linear and nonlinear input/output
relations. It will be of special interest to researchers, engineers and
graduate students who have specialized in ?ltering theory and system
theory. From noisy or noiseless data,
reductionwillbemade.Anewmethodwhichreducesnoiseormodelsinformation will
be proposed. Using this method will allow model description to be
treated as noise reduction or model reduction. As proof of the e?cacy,
this monograph provides new results and their extensions which can also
be applied to nonlinear dynamical systems. To present the e?ectiveness
of our method, many actual examples of noise and model information
reduction will also be provided. Using the analysis of state space
approach, the model reduction problem may have become a major theme of
technology after 1966 for emphasizing e?ciency in the ?elds of control,
economy, numerical analysis, and others. Noise reduction problems in the
analysis of noisy dynamical systems may
havebecomeamajorthemeoftechnologyafter1974foremphasizinge?ciencyin
control.However, thesubjectsoftheseresearcheshavebeenmainlyconcentrated
in linear systems. In common model reduction of linear systems in use
today, a singular value
decompositionofaHankelmatrixisusedto?ndareducedordermodel.However, the
existence of the conditions of the reduced order model are derived
without
evaluationoftheresultantmodel.Inthecommontypicalnoisereductionoflinear
systems in use today, the order and parameters of the systems are
determined by minimizing information criterion. Approximate and noisy
realization problems for input/output relations can be roughly stated as
follows: A. The approximate realization problem. For any input/output
map, ?nd one mathematical model such that it is similar
totheinput/outputmapandhasalowerdimensionthanthegivenminimalstate
spaceofadynamicalsystemwhichhasthesamebehaviortotheinput/outputmap. B.
The noisy realization problem
