## Preliminary list of abstracts

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*Keywords:*Parametric model order reduction

- Benner, Peter (Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Germany)

Parametric model order reduction (PMOR) has become an important tool in computing surrogate models of parameter-dependent, dynamical systems to be used in design optimization and control. PMOR can be considered as an approximation problem for a special multi-parametric function. For this purpose, we employ a connection between linear parametric and bilinear control systems which allows for several efficient approximation techniques. Here, we will focus on a generalization of the method of balanced truncation for linear systems which leads to large-scale Lyapunov equations of the form $$AX+XA^T+\sum_{j=1}^mN_jXN_j^T+BB^T=0,$$ with $A,N_j \in \mathbb R^{n\times n}$ and $B \in \mathbb R^{n\times m}.$ Imposing some assumptions on $N_j$ and $B,$ we will make use of the corresponding tensorized version $$\left(I\otimes A +A\otimes I + \sum_{j=1}^mN_j\otimes N_j\right)\operatorname{vec}{(X)}=-\operatorname{vec}{(BB^T)}$$ to show the existence of low-rank approximations to the solution matrix $X.$ Finally, this will justify extending low-rank methods like e.g. the ADI iteration or other rational Krylov subspace methods which are known to be effective tools in the linear case. By means of a numerical example, we will evaluate the performance of those methods.