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dc.contributor.authorZigic, Draganen_US
dc.contributor.authorWatson, Layne T.en_US
dc.contributor.authorCollins, Emmanuel G.en_US
dc.contributor.authorBernstein, Dennis S.en_US
dc.date.accessioned2013-06-19T14:36:21Z
dc.date.available2013-06-19T14:36:21Z
dc.date.issued1991
dc.identifierhttp://eprints.cs.vt.edu/archive/00000269/en_US
dc.identifier.urihttp://hdl.handle.net/10919/19691
dc.description.abstractThe optimal projection approach to solving the H2 reduced order model problem produces two coupled, highly nonlinear matrix equations with rank conditions as constraints. The algorithms proposed herein utilize probability-one homotopy theory as the main tool. It is shown that there is a family of systems (the homotopy) that make a continuous transformation from some initial system to the final system. With a carefully chosen initial system all the systems along the homotopy path will be asymptotically stable, controllable and observable. One method, which solves the matrix equations in their original form, requires a decomposition of the projection matrix using the Drazin inverse of a matrix. An effective algorithm for computing the derivative of the projection matrix that involves solving a set of Sylvester equations is given. Several strategies for choosing the homotopy maps and the starting points (initial systems) are discussed and compared, in the context of some reduced order model problems from the literature. Numerical results are included for ten test problems, of sizes 2 through 17.en_US
dc.format.mimetypeapplication/pdfen_US
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen_US
dc.relation.ispartofHistorical Collection(Till Dec 2001)en_US
dc.titleHomotopy Approaches to the H2 Reduced Order Model Problemen_US
dc.typeTechnical reporten_US
dc.identifier.trnumberTR-91-24en_US
dc.type.dcmitypeTexten_US
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000269/01/TR-91-24.pdf


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