Negative imaginary balancing for mode reduction of LTI negative imaginary systems

In this paper, we are dedicated to solve the model order reduction problems of negative imaginary linear-time invariant (LTI) systems in the balancing-related framework. A negative imaginary balanced truncation algorithm was proposed, wherein solving negative imaginary Lur´e equations or Riccati equations is involved. It is shown that the algorithm generate negative imaginary preserving reduced-order model, besides, the issue of approximation error between the original system and the reduced-order model was discussed and a multiplicative type error bound was provided. Finally, a numerical example is included for illustration.