Krylov subspace methods for model order reduction of bilinear control systems

We discuss the use of Krylov subspace methods with regard to the problem of model order reduction. The focus lies on bilinear control systems, a special class of nonlinear systems, which are closely related to linear systems. While most existent approaches are based on series expansions around zero, we will extend the underlying ideas to a more general context and show that there exist several ways to reduce bilinear systems. Besides, we will briefly address the problem of stability preserving model reduction and further explain the benefit of using two-sided projection methods. By means of some numerical examples, we will illustrate the performance of the presented reduction methods.