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This talk will present recent advances in mathematical
modeling of dynamical systems, with a focus on methods of model reduction
and their impact on the analysis and simulation of complex engineering
systems.
Recent analytical developments are presented that lead to mathematical
criteria for measuring the similarity of system models. Model reduction
methods are introduced which result in a reduction in the dimensions of
a model, and for which a-priori guaranteed error bounds are satisfied.
New results and tools for analysis of time varying systems are introduced,
and the general methodology, results and current activity are discussed.
The technical machinery is developed in an operator theory setting; applications
include finite-element models of mechanics and aircraft control systems.
We also present some recent extensions to multidimensional and spacetime
representations of systems.
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