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Robust Static Output Feedback \(H_{\infty }\) Controller Design for Linear Parameter-Varying Time Delay Systems

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Abstract

This paper addresses the problem of synthesizing an \(H_{\infty }\) static output feedback controller for linear parameter-varying (LPV) time delay systems subject to time-varying delay. The motivation for this research stems from the challenges associated with designing controllers for such systems. In addition to considering the static output feedback controller design, we also explore the design of a dynamic output feedback controller within the context of \(H_{\infty }\) control. This is achieved by augmenting the system dynamics with the inclusion of the dynamic controller state and formulating the dynamic output feedback controller in an equivalent form of static output feedback control for the overall system. To tackle the synthesis problem, a quadratic Lyapunov–Krasovskii functional is selected, and a sufficient matrix inequality condition is developed by utilizing the well-known Jensen-type integral inequality. This approach enhances the robustness of the controller design and accounts for the time-varying delay characteristics of the system. An iterative algorithm is introduced to efficiently search for a potential feasible solution set of the synthesis problem. The effectiveness of the proposed controller design methods is demonstrated through several numerical examples. The application of the proposed approaches is showcased, and a comparative analysis is performed. Specifically, the results are compared with the existing approaches in the literature, considering both dynamic output feedback controllers and static output feedback controllers for \(H_{\infty }\) control. This comparison highlights the advantages and differences of the proposed methodology. Overall, this research contributes to the field by offering systematic methodologies for synthesizing \(H_{\infty }\) static output feedback controllers for LPV time delay systems subject to time-varying delay. The incorporation of dynamic output feedback controller design provides additional insights and flexibility. The numerical examples validate the applicability of the proposed methods and underscore their potential advantages in terms of robustness and performance.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The author generated this text in part with GPT-3, OpenAI’s large-scale language-generation model. Upon generating draft language, the author reviewed, edited, and revised the language to his own liking and takes ultimate responsibility for the content of this publication.

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  1. Department of Electrical and Electronics Engineering, Faculty of Engineering and Natural Sciences, İstanbul Bilgi University, Istanbul, Turkey

    Mehmet Nur Alpaslan Parlakci

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  1. Mehmet Nur Alpaslan Parlakci
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Parlakci, M.N.A. Robust Static Output Feedback \(H_{\infty }\) Controller Design for Linear Parameter-Varying Time Delay Systems. Circuits Syst Signal Process 43, 843–864 (2024). https://doi.org/10.1007/s00034-023-02514-z

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