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In this contribution, we discuss the modeling and model reduction frameworkknown as the Loewner framework. This is a data-driven approach, applicable tolarge-scale systems, which was originally developed for applications to lineartime-invariant systems. In recent years, this method has been extended to anumber of additional more complex scenarios, including linear parametric ornonlinear dynamical systems. We will provide here an overview of the lattertwo, together with time-domain extensions. Additionally, the application of theLoewner framework is illustrated by a collection of practical test cases.Firstly, for data-driven complexity reduction of the underlying model, andsecondly, for dealing with control applications of complex systems (inparticular, with feedback controller design).

Data-driven modeling and control of large-scale dynamical systems in the Loewner framework