H2 model reduction for negative imaginary systems. Issue 3 (3rd March 2020)

• Record Type: Journal Article
• Authors: Yu, Lanlin; Xiong, Junlin
• Is Part Of: International journal of control. Volume 93:Issue 3(2020)
• Page Start: 588
• Page End: 598
• Publication Date: 2020-03-03
• Subjects: Negative imaginary systems -- H2 model reduction -- optimisation -- Stiefel manifold; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1482501
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : This paper studies the H 2 model reduction problem for negative imaginary (NI) systems. For a given high-order system that is stable and NI, our goal is to approximate it by a low-order NI system so that the H 2 norm of the approximation error system is minimised. By using the Galerkin projection, the H 2 model reduction problem is formulated as a minimisation problem over the Stiefel manifold. The first-order necessary condition is derived for the construction of a local optimal reduced-order system. A gradient descent algorithm is provided to solve the first-order necessary condition. The resulting reduced-order system preserves the stability and the NI structure of the original system. Finally, two examples are presented to demonstrate the effectiveness of the proposed H 2 model reduction method.