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Electrical Engineering and Systems Science > Systems and Control

arXiv:2203.13603 (eess)
[Submitted on 25 Mar 2022 (v1), last revised 5 Sep 2022 (this version, v2)]

Title:Making Nonlinear Systems Negative Imaginary via State Feedback

Authors:Kanghong Shi, Ian R. Petersen, Igor G. Vladimirov
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Abstract:This paper provides a state feedback stabilization approach for nonlinear systems of relative degree less than or equal to two by rendering them nonlinear negative imaginary (NI) systems. Conditions are provided under which a nonlinear system can be made a nonlinear NI system or a nonlinear output strictly negative imaginary (OSNI) system. Roughly speaking, an affine nonlinear system that has a normal form with relative degree less than or equal to two, after possible output transformation, can be rendered nonlinear NI and nonlinear OSNI. In addition, if the internal dynamics of the normal form are input-to-state stable, then there exists a state feedback input that stabilizes the system. This stabilization result is then extended to achieve stability for systems with a nonlinear NI uncertainty.
Comments: 10 pages, 2 figures
Subjects: Systems and Control (eess.SY)
Cite as: arXiv:2203.13603 [eess.SY]
  (or arXiv:2203.13603v2 [eess.SY] for this version)
  https://doi.org/10.48550/arXiv.2203.13603

Submission history

From: Kanghong Shi [view email]
[v1] Fri, 25 Mar 2022 12:03:24 UTC (266 KB)
[v2] Mon, 5 Sep 2022 06:45:56 UTC (267 KB)
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