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Frequency- and time-limited balanced truncation for large-scale second-order systems. (English) Zbl 07355232
Summary: Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefore, it usually pays off to compute local approximations of the used dynamical systems in the frequency and time domain. In this paper, we consider a structure-preserving extension of the frequency- and time-limited balanced truncation methods to second-order dynamical systems. We give a full overview about the first-order limited balanced truncation methods and extend those to second-order systems by using the different second-order balanced truncation formulas from the literature. Also, we present numerical methods for solving the arising large-scale sparse matrix equations and give numerical modifications to deal with the problematic case of second-order systems. The results are then illustrated on three numerical examples.
MSC:
93B11 System structure simplification
93C70 Time-scale analysis and singular perturbations in control/observation systems
93C80 Frequency-response methods in control theory
93C05 Linear systems in control theory
93A15 Large-scale systems
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