H2 model reduction for negative imaginary systems

Abstract

This paper studies the 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 norm of the approximation error system is minimised. By using the Galerkin projection, the 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 model reduction method.