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From Time-Domain Data to Low-Dimensional Structured Models
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We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of the system. We estimate the transfer function of the original model at selected frequencies using a modification of the empirical transfer function estimation that was recently presented in [Peherstorfer, Gugercin, Willcox, SIAM J. Sci. Comput., 39(5):2152-2178, 2017]. Our realization interpolates the transfer function estimates and can be seen as a generalization of the Loewner framework to structured systems. We demonstrate the presented framework by means of a delay example.
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The Pantelides algorithm for delay differential-algebraic equations
A graph algorithm with equivalence classes extends the Pantelides structural analysis from DAEs to delay differential-algebraic equations and gives a necessary and sufficient termination condition.
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