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Applied mathematics, Electrical and electronic engineering
For efficient simulation of state-of-the-art dynamical systems as arise in all aspects of engineering, the development of reduced-order models is of paramount importance. While linear reduction techniques have received considerable study, increasingly nonlinear model reduction is becoming a significant field of interest. From a circuits and systems viewpoint, systems involving micromachined devices or systems involving mixed technologies necessitate the development of reduced-order nonlinear models. From a control systems viewpoint, the design of controllers for nonlinear systems is greatly facilitated by nonlinear model reduction strategies. To this end, the paper proposes two novel model-reduction strategies for nonlinear systems. The first involves the development, in a novel manner as compared to previous approaches, of a reduced-order model from a bilinear representation of the system while the second involves a reducing a polynomial approximation using subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example.
M. Condon, R. Ivanov, Krylov subspaces from bilinear representations of nonlinear systems, COMPEL Journal, Vol. 26, Issue 2, 2007