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Robust stabilization of LTI negative imaginary systems using the nearest negative imaginary controller

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submitted on 2024-02-19, 09:58 and posted on 2024-02-19, 12:39 authored by Mohamed Mabrok, Mahmoud Abdelrahim

This paper considers the problem of robust stabilization of linear time‐invariant systems with respect to unmodelled dynamics and structure uncertainties. To that end, a methodology to find the nearest negative imaginary system for a given non‐negative imaginary system is presented first. Then, this result is employed to construct a near optimal linear quadratic Gaussian controller achieving desired performance measures. The problem is formulated using port‐Hamiltonian method and the required conditions are defined in terms of linear matrix inequalities. The technique is presented using the fast gradient method to solve the problem systematically. The designed controller satisfies a negative imaginary property and guarantees a robust feedback loop. The effectiveness of the approach is demonstrated by a simulation on a numerical example.

Other Information

Published in: IET Control Theory & Applications
License: http://creativecommons.org/licenses/by/4.0/
See article on publisher's website: https://dx.doi.org/10.1049/cth2.12578

Funding

Open Access funding provided by the Qatar National Library.

History

Language

  • English

Publisher

Institution of Engineering and Technology

Publication Year

  • 2023

License statement

This Item is licensed under the Creative Commons Attribution 4.0 International License.

Institution affiliated with

  • Qatar University
  • College of Arts and Sciences - QU

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