Energy estimates and model order reduction for stochastic bilinear systems

Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems

We discuss the relation of a certain type of generalized Lyapunov equations to Gramians of stochastic and bilinear systems together with the corresponding energy functionals. While Gramians and energy functionals of stochastic linear systems show a strong correspondence to the analogous objects for deterministic linear systems, the relation of Gramians and energy functionals for bilinear system...

Balanced Truncation Model Order Reduction for Quadratic-bilinear Control Systems

We discuss balanced truncation model order reduction for large-scale quadraticbilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and observability Gramians. These Gramians are extended to a general nonlinear setting in Scherpen (1993), where it is shown that Gramians for nonlinear systems are the solut...

A Note on Projection Techniques for Model Order Reduction of Bilinear Systems

In this paper we review two recently suggested projection techniques for model order reduction of bilinear systems. The first one is computationally more attractive, but so far it was assumed that this method does not yield a moment-matching approximation. Here we show that the reduced-order models computed by both of the two projection techniques match multimoments of the bilinear system. This...

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 ...

Interpolation Methods for the Model Reduction of Bilinear Systems