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

Kanghong Shi, Ian R. Petersen, Igor G. Vladimirov

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

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