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Balanced truncation model reduction for linear time-varying systems

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  • N. Lang
  • J. Saak
  • T. Stykel

Abstract

A practical procedure based on implicit time integration methods applied to the differential Lyapunov equations arising in the square root balanced truncation method is presented. The application of high-order time integrators results in indefinite right-hand sides of the algebraic Lyapunov equations that have to be solved within every time step. Therefore, classical methods exploiting the inherent low-rank structure often observed for practical applications end up in complex data and arithmetic. Avoiding the additional effort in treating complex quantities, a symmetric indefinite factorization of both the right-hand side and the solution of the differential Lyapunov equations is applied.

Suggested Citation

  • N. Lang & J. Saak & T. Stykel, 2016. "Balanced truncation model reduction for linear time-varying systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 22(4), pages 267-281, July.
    • Handle: RePEc:taf:nmcmxx:v:22:y:2016:i:4:p:267-281
    DOI: 10.1080/13873954.2016.1198386
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    References listed on IDEAS

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    1. Peter Benner & Patrick Kürschner & Jens Saak, 2013. "An improved numerical method for balanced truncation for symmetric second-order systems," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 19(6), pages 593-615, December.
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