Abstract
The computation of \(\mathscr {H}_2\) and \(\mathscr {H}_{2,\varOmega }\) 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 \(\mathscr {H}_2\) model reduction for TDS, based on the ideas provided in [3], 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.
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Pontes Duff, I., Vuillemin, P., Poussot-Vassal, C., Briat, C., Seren, C. (2016). Model Reduction for Norm Approximation: An Application to Large-Scale Time-Delay Systems. In: Seuret, A., Hetel, L., Daafouz, J., Johansson, K. (eds) Delays and Networked Control Systems . Advances in Delays and Dynamics, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-32372-5_3
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