Second-order balanced truncation

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Model reduction of second order systems (2005, methodology): “The following result can be found in a slightly different form in [4].”
Comparison of model reduction techniques for large mechanical systems (2008, unknown): “Balancing-related truncation techniques [2, 10, 16–18].”
Balanced truncation model reduction of second-order systems (2008, methodology): “Such components are less involved in the energy transfer from inputs to outputs, see [10, 15] for details.”
An improved numerical method for balanced truncation for symmetric second-order systems (2013, background): “Some more recent adaptions take the second-order structure of (1) into account [2,4,5].”
Simulation process of flexible multibody systems with non-modal model order reduction techniques (2011, background): “A similar result can be obtained for the position observability Gramian matrix Qp by using the dual system; see [17, 38].”