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arxiv: 1902.01652 · v1 · pith:SW5WMHWWnew · submitted 2019-02-05 · 🧮 math.NA

Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systems

Igor Pontes Duff , Patrick K\"urschner This is my paper
classification 🧮 math.NA
keywords boundsnumericalsystemsbalanceddiscrete-timelarge-scaleoutputtime
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In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the approximated output vector within the time limits. The influence of different components in the established bounds will be highlighted. After that, the second part of the article proposes strategies that enable an efficient numerical execution of time-limited balanced truncation for large-scale systems. Numerical experiments illustrate the performance of the proposed techniques.

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  1. An $L^2_T$-error bound for time-limited balanced truncation

    math.OC 2019-07 unverdicted novelty 7.0

    Derives an L²_T-error bound for time-limited balanced truncation that converges to the H∞ bound as T→∞ and yields a short proof of the unrestricted case.