A note on modeling some classes of nonlinear systems from data

We study the modeling of bilinear and quadratic systems from measured data. The measurements are given by samples of higher order frequency response functions. These values can be identified from the corresponding Volterra series of the underlying nonlinear system. We test the method for examples from structural dynamics and chemistry

Loewner functions for bilinear systems

This work brings together the moment matching approach based on Loewner functions and the classical Loewner framework based on the Loewner pencil in the case of bilinear systems. New Loewner functions are defined based on the bilinear Loewner framework, and a Loewner equivalent model is produced using these functions. This model is composed of infinite series that needs to be truncated in order to be implemented in practice. In this context, a new notion of approximate Loewner equivalence is introduced. In the end, it is shown that the moment matching procedure based on the proposed Loewner functions and the classical interpolatory bilinear Loewner framework both result in $\kappa$-Loewner equivalent models, the main difference being that the latter preserves bilinearity at the expense of a higher order

Model reduction of linear hybrid systems

The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on balanced truncation. Moreover, the paper also proves an analytical error bound for the difference between the input-output behaviors of the original and the reduced order model. This error bound is formulated in terms of singular values of the Gramians used for model reduction