Dynamic Parallel Feedforward Compensator-based Generalized Negative Imaginary Synthesis Allowing Poles At The Origin *

This paper presents a new negative imaginary(NI) synthesis method for a linear-time-invariant(LTI) system with up to two poles at the origin. A dynamic parallel feedforward compensator(DPFC) is added to the controlled plant, which ensures that the augmented system exhibits generalized negative imaginary(GNI) property. And a set of linear matrix inequalities(LMIs) conditions are derived, leading to easy application of this scheme. The augmented system could be stabilized by any SNI controllers only if satisfying the DC loop gain condition. As an application of these results, an example of stabilizing a flexible satellite is carried out to verify the effectiveness of the proposed method.