Model order reduction for bilinear systems with non-zero initial states -- different approaches with error bounds

TL;DR

This paper explores model order reduction techniques for bilinear systems with non-zero initial states, analyzing different approaches with error bounds and stability considerations, including new criteria for subsystem stability and Gramians.

Contribution

It introduces novel strategies for reducing bilinear systems with non-zero initial conditions, providing error bounds and stability criteria for each approach.

Findings

Error bounds depend on truncated Hankel singular values.

New stability criterion ensures existence of Gramians and system stability.

Multiple reduction strategies are proposed for bilinear systems with initial states.

Abstract

In this paper, we consider model order reduction for bilinear systems with non-zero initial conditions. We discuss choices of Gramians for both the homogeneous and the inhomogeneous parts of the system individually and prove how these Gramians characterize the respective dominant subspaces of each of the two subsystems. Proposing different, not necessarily structure preserving, reduced order methods for each subsystem, we establish several strategies to reduce the dimension of the full system. For all these approaches, error bounds are shown depending on the truncated Hankel singular values of the subsystems. Besides the error analysis, stability is discussed. In particular, a focus is on a new criterion for the homogeneous subsystem guaranteeing the existence of the associated Gramians and an asymptotically stable realization of the system.