Large-scale dynamical model approximation and its applications ; Approximation de modèle de grande dimension et applications

Linear dynamical models play an important role in many engineering fields, including simulation, analysis, optimization and control of complex systems and processes. This role is emphasized when critical systems are under consideration, and for which a deep attention and understanding are needed. Among others, this attention may be motivated by industrial, economical, societal and strategical reasons. Indeed, for these cases, digital-based solutions involving dedicated computer-based softwares are being developed and largely preferred by engineers and researchers to reduce development costs and time, to improve and to better understand the systems under consideration. These systems being largely grounded on accurate complex and large-scale dynamical models, not well adapted to standard numerical tool and computationally demanding, their approximation by an (accurate) low complexity dynamical model is then a cornerstone for further advanced developments.This manuscript addresses this last point, namely, the linear large-scale (and infinite dimensional) dynamical model approximation. Moreover, many research and industrial applications are detailed, illustrating the wide application spectrum of this research field. More specifically, the interpolatory framework, tailored to a large variety of dynamical model structures and classes, is the main tool invoked. Moreover, as side effect of the main purpose of dynamical model approximation, extensions to the approximation of the input-output stability regions of a class of meromorphic functions is also presented, highlighting the effectiveness and versatility of the methods developed within this research field