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Making nonlinear systems negative imaginary via state feedback✩
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DOI：10.1016/j.automatica.2023.111127.png)
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Abstract
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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 input-affine nonlinear system can be rendered nonlinear NI and nonlinear OSNI if it has a normal form with relative degree less than or equal to two after possible output transformation. 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. A numerical example is provided to illustrate the process of stabilizing an uncertain system using the proposed results. & COPY; 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords:
Nonlinear negative imaginary (NI) system
systems
State feedback stabilization
Robust control
State feedback equivalence to nonlinear NI
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