# Necessary and Sufficient Conditions for State Feedback Equivalence to Negative Imaginary Systems

arXiv: https://arxiv.org/abs/2109.11273 · HTML: https://mlsanity.com/paper/2109.11273/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [Negative Imaginary Neural ODEs: Learning to Control Mechanical Systems with Stability Guarantees](https://mlsanity.com/paper/2504.19497/) (2025)

## Abstract (arXiv)

In this paper, we present necessary and sufficient conditions under which a linear time-invariant (LTI) system is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show that a minimal LTI strictly proper system can be rendered NI using full state feedback if and only if it can be output transformed into a system, which has relative degree less than or equal to two and is weakly minimum phase. We also considered the problems of state feedback equivalence to output strictly negative imaginary systems and strongly strict negative imaginary systems. Then we apply the NI state feedback equivalence result to robustly stabilize an uncertain system with strictly negative imaginary uncertainty. An example is provided to illustrate the proposed results, for the purpose of stabilizing an uncertain system.