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This paper presents necessary and sufficient conditions under which a linearsystem of relative degree either one or two is state feedback equivalent to anegative imaginary (NI) system. More precisely, we show for a class of lineartime-invariant strictly proper systems, that such a system can be renderedminimal and NI using full state feedback if and only if it is controllable andweakly minimum phase. A strongly strict negative imaginary state feedbackequivalence result is also provided. The NI state feedback equivalence resultis then applied in a robust stabilization problem for an uncertain system witha strictly negative imaginary uncertainty.

Negative Imaginary State Feedback Equivalence for Systems of Relative Degree One and Relative Degree Two