Time-domain moment matching model reduction for negative imaginary systems

In this paper, the moment matching model reduction problem for negative imaginary systems is considered in the time-domain framework. For a given high order negative imaginary system with poles at the origin, our goal is to find a reduced-order negative imaginary system such that a prescribed number of the moments and the poles at the origin are preserved. The reduced-order negative imaginary systems was constructed by the parameterized reduced-order systems that match the moments. It shows that a desired reduced-order system can be obtained by using the unique solution of a Sylvester equation. Finally, the proposed model reduction method is illustrated by an RLC network and a train system.