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

2021/03/09 by Kanghong Shi, Shi, Kanghong, Ian R. Petersen +3 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC

paper · pdf · doi:10.48550/arxiv.2103.05249

12 pages, 2 figures

arxiv created 2021/11/04 · arxiv updated 2021/11/05

Abstract

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 NI using full state feedback if and only if it is controllable and weakly minimum phase. A strongly strict negative imaginary 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 uncertainty.

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

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