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Model reduction for norm approximation: an application to large-scale time-delay systems. (English) Zbl 1355.93033

Seuret, Alexandre (ed.) et al., Delays and networked control systems. Cham: Springer (ISBN 978-3-319-32371-8/hbk; 978-3-319-32372-5/ebook). Advances in Delays and Dynamics 6, 37-55 (2016).
Summary: The computation of \(\mathcal {H}_2\) and \(\mathcal {H}_{2,\varOmega}\) norms for LTI Time-Delay Systems (TDS) are important challenging problems for which several solutions have been provided in the literature. Several of these approaches, however, cannot be applied to systems of large dimension because of the inherent poor scalability of the methods, e.g., LMIs or Lyapunov-based approaches. When it comes to the computation of frequency-limited norms, the problem tends to be even more difficult. In this chapter, a computationally feasible solution using \(\mathcal {H}_2\) model reduction for TDS, based on the ideas provided in [C. Beattie and S. Gugercin, “Realization-independent \(\mathcal H_2\)-approximation”, in: IEEE 51st annual conference on decision and control, CDC 2012. Los Alamitos: IEEE Computer Society. 4953–4958 (2012; doi:10.1109/CDC.2012.6426344)], is proposed. It is notably demonstrates on several examples that the proposed method is suitable for performing both accurate model reduction and norm estimation for large-scale TDS.
For the entire collection see [Zbl 1357.93004].

MSC:

93A15 Large-scale systems
93B11 System structure simplification
93C05 Linear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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