A New Stability Result for the Feedback Interconnection of Negative Imaginary Systems with a Pole at the Origin

TL;DR

This paper establishes new stability conditions for negative imaginary systems with poles at the origin, extending existing lemmas to include such cases and providing practical criteria for stability.

Contribution

It generalizes the negative imaginary lemma to systems with poles at the origin and offers a new sufficient stability condition for their feedback interconnections.

Findings

Derived a generalized negative imaginary lemma including poles at the origin

Provided a new sufficient condition for internal stability of NI systems with poles at the origin

Supported results with an illustrative example

Abstract

This paper is concerned with stability conditions for the positive feedback interconnection of negative imaginary systems. A generalization of the negative imaginary lemma is derived, which remains true even if the transfer function has poles on the imaginary axis including the origin. A sufficient condition for the internal stability of a feedback interconnection for NI systems including a pole at the origin is given and an illustrative example is presented to support the result.