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Model Reduction by Moment Matching at Poles for Linear and Nonlinear Systems

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This talk is divided in two parts. The first part of the talk is focused on the model reduction problem for continuous-time, linear, time-invariant systems at poles of the transfer function. The notion of moment is first extended to poles of the transfer function, where moments are classically not defined. The moments at a pole of the transfer function are then shown to be uniquely specified by the solution of certain Sylvester equations. This allows to construct reduced order models which preserve given poles and match the corresponding moments. In the second part of the talk, the classical notions of eigenvalue and of pole of a linear system are revisited adopting a geometric approach and extended to nonlinear systems. The proposed definitions are then used to pose and solve the model reduction problem at poles for nonlinear systems. The theory is illustrated by means of simple worked-out examples.

This talk is part of the CUED Control Group Seminars series.

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