4 papers
L2-L2-gain bounds for quadratic output systems
Birgit Hillebrecht
We derive an explicit bound for the L2-L2-gain of linear time-invariant systems whose output is a quadratic function of the state and the input. Such systems appear naturally in ma…
model order reduction for quadratic output systems
Birgit Hillebrecht, Benjamin Unger
Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturall…
Estimation of the input-to-state stability gain functions from finite-dimensional approximations
Birgit Hillebrecht, Benjamin Unger
Since the concept of input-to-state stability (ISS) was introduced, it has been extensively investigated for finite-dimensional control systems and has recently received attention…
Prediction error certification for PINNs: Theory, computation, and application to Stokes flow
Birgit Hillebrecht, Benjamin Unger
Rigorous error estimation is a fundamental topic in numerical analysis. With the increasing use of physics-informed neural networks (PINNs) for solving partial differential equatio…