Reduced order models, or model reduction, have been used in many
technologically advanced areas to ensure the associated complicated
mathematical models remain computable. For instance, reduced order
models are used to simulate weather forecast models and in the
design of very large scale integrated circuits and networked
dynamical systems. For linear systems, the model reduction problem
has been addressed from several perspectives and a comprehensive
theory exists. Although many results and efforts have been made, at
present there is no complete theory of model reduction for
nonlinear systems or, at least, not as complete as the theory
developed for linear systems. This monograph presents, in a uniform
and complete fashion, moment matching techniques for nonlinear
systems. This includes extensive sections on nonlinear time-delay
systems; moment matching from input/output data and the limitations
of the characterization of moment based on a signal generator
described by differential equations. Each section is enriched with
examples and is concluded with extensive bibliographical notes.
This monograph provides a comprehensive and accessible introduction
into model reduction for researchers and students working on
non-linear systems.
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