Structure-Preserving Model Reduction of Negative Imaginary Systems

This paper presents a structure-preserving model reduction framework for negative imaginary (NI) systems based on a state-space parametrisation. We first establish a constructive representation showing that any NI system without poles at the origin can be parametrised by a skew-symmetric, a positive semi-definite, an arbitrary, and a symmetric matrix, thereby revealing the internal state-space structure underlying the NI property. Leveraging this parametrisation, a projection-based model reduction method is developed that guarantees both the preservation of the NI property and exact interpolation of the transfer function at prescribed frequency points. Numerical examples on flexible structures are presented to demonstrate the validity of the proposed parametrisation, the interpolation accuracy and structure-preserving capability of the proposed method.