For second-order systems with proportional damping, the reduced matrices of balanced truncation can be assembled directly from frequency-response samples via explicit formulas and solved efficiently with low-rank Sylvester equations.
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Data-driven balanced truncation for second-order systems via the approximate Gramians
For second-order systems with proportional damping, the reduced matrices of balanced truncation can be assembled directly from frequency-response samples via explicit formulas and solved efficiently with low-rank Sylvester equations.