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

Interpolatory Weighted-H2 Model Reduction

This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an optimal reduced-order model. The H2 norm representation also provides an error expression that motivates a new weighted-H2 model reduction algorithm. Several numerical examples illustrate the effectiveness of the proposed approach

A survey of model reduction by balanced truncation and some new results

Abstract Balanced truncation is one of the most common model reduction schemes. In this note, we present a survey of balancing related model reduction methods and their corresponding error norms, and also introduce some new results. Five balancing methods are studied: (1) Lyapunov balancing, (2) Stochastic balancing (3) Bounded real balancing, (4) Positive real balancing and (5) Frequency weighted balancing. For positive real balancing, we introduce a multiplicative-type error bound. Moreover, for a certain subclass of positive real systems, a modi£ed positive-real balancing scheme with an absolute error bound is proposed. We also develop a new frequencyweighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system gramians. Two numerical examples are illustrated to verify the ef£ciency of the proposed methods

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

A duality perspective on Loewner rational interpolation and state-space modelling of vector-exponential trajectories

We explore some connections between the Loewner approach to interpolation and realization, and that based on bilinear differential forms arising in the behavioral framework. We show that a crucial concept underlying both approaches is that of duality of trajectories, and that many known results can be interpreted in its ligh