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Considering the use of dynamical systems in practical applications, oftenonly limited regions in the time or frequency domain are of interest. Therefor,it usually pays off to compute local approximations of the used dynamicalsystems in the frequency and time domain. In this paper, we consider astructure-preserving extension of the frequency- and time-limited balancedtruncation methods to second-order dynamical systems. We give a full overviewabout the first-order limited balanced truncation methods and extend thosemethods to second-order systems by using the different second-order balancedtruncation formulas from the literature. Also, we present numerical methods forsolving the arising large-scale sparse matrix equations and give numericalmodifications to deal with the problematic case of second-order systems. Theresults are then illustrated on three numerical examples.

Frequency- and Time-Limited Balanced Truncation for Large-Scale Second-Order Systems