Model Order Reduction for (Stochastic-) Delay Equations With Error Bounds

TL;DR

This paper develops a structure-preserving model order reduction method for delay and stochastic delay equations, providing new error bounds and a system theoretic interpretation, enhancing accuracy and understanding of reduced models.

Contribution

It introduces a novel model reduction technique for delay and stochastic delay systems with explicit error bounds and a system theoretic framework, extending previous methods.

Findings

Derived new error bounds for delay systems using Hankel operator transfer

Extended error analysis to bilinear and stochastic systems with noise

Provided a system theoretic interpretation of the reduction technique

Abstract

We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel operators to delay systems, we find error estimates for the difference between the dynamics of the full and reduced model. This analysis also yields new error bounds for bilinear systems and stochastic systems with multiplicative noise and non-zero initial states.