H2 model order reduction: A relative error setting

Umair Zulfiqar, Xin Du, Qiu Yan Song, Muwahida Liaquat, Victor Sreeram

Research output: Contribution to journalArticlepeer-review


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 systems. 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 reduces 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.

Original languageEnglish
Article number105745
Number of pages10
JournalSystems and Control Letters
Early online date6 Feb 2024
Publication statusPublished - Mar 2024


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