H2 Model Order Reduction: A Relative Error Setting

TL;DR

This paper introduces an oblique projection algorithm for model order reduction that minimizes the H2 norm of the relative error, offering improved accuracy and computational efficiency over existing methods.

Contribution

It presents a novel algorithm for reducing system order by directly minimizing the relative error in the H2 norm, avoiding large-scale Riccati and Lyapunov equations.

Findings

Algorithm compares well with balanced stochastic truncation in accuracy.

Avoids solving large-scale Riccati and Lyapunov equations.

Numerical simulations confirm effectiveness.

Abstract

In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system norms of additive or relative error system. The relative error is a superior criterion to the additive error in assessing accuracy in many applications like reduced-order controller and filter designs. In this paper, we propose an oblique projection algorithm that minimizes the H2 norm of the relative error transfer function. The selection of reduction matrices in the algorithm is motivated by the necessary conditions for local optima of the (squared) H2 norm of the relative error transfer function. Numerical simulation confirms that the proposed algorithm compares well in accuracy with balanced stochastic truncation while avoiding the solution of large-scale Riccati and Lyapunov equations.