Preprint No. MPIMD/13-02

Title: Balanced Truncation of Linear Time-Invariant Systems at a Single Frequency

Author(s): Xin Du, Peter Benner, Guanghong Yang, Dan Ye


Date: 2013-01-30


This work considers the model reduction of linear time-invariant systems with focus on good approximation at a particular frequency. A family of frequency-dependent extended systems preserving some special frequency-dependent properties is constructed first, then the corresponding controllability and observability Lyapunov equations are defined. Finally, those results are used to develop the desired frequency-dependent balanced truncation, which generates the desired reduced-order model with an explicit frequency-dependent approximation error bound. Both continuous-time and discrete-time systems are considered. Several benchmark examples are tested to illustrate the advantage of the proposed frequency-dependent balanced truncation method.


author = {Xin Du and Peter Benner and Guanghong Yang and Dan Ye},
title = {Balanced Truncation of Linear Time-Invariant Systems at a Single Frequency},
number = {MPIMD/13-02},
month = jan,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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