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Event-triggered \(H_{\infty }\) controller design for uncertain fractional-order systems with time-varying delays

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Abstract

The primary focus of this paper is to investigate the \(H_{\infty }\) state feedback control problem within uncertain fractional-order systems characterized by time-varying delays. Our approach centers on the development of an event-triggered \(H_{\infty }\) control strategy, facilitated by the refined fractional-order Razumikhin theorem. This strategy is aimed at ensuring the uniformly asymptotic stability of the controlled system while adhering to a predefined \(H_{\infty }\) performance index. The central challenge lies in the memory characteristics of the fractional-order calculus operator, particularly in the context of delayed fractional-order systems, where preventing the occurrence of the Zeno phenomenon is paramount. To address this challenge, we introduce a novel theoretical framework and establish a new condition to prevent Zeno behaviors. This condition is derived using inequality techniques and leverages several essential properties of fractional-order calculus. To verify the effectiveness and feasibility of our proposed method, we present two illustrative examples.

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Acknowledgements

The author would like to thank the editor(s) and anonymous reviewers for their constructive comments which helped to improve the present paper. The research is funded by the Ministry of Education and Training of Vietnam under Grant Number B2023-TNA-15.

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Correspondence to Mai Viet Thuan.

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Sau, N.H., Binh, T.N., Thanh, N.T. et al. Event-triggered \(H_{\infty }\) controller design for uncertain fractional-order systems with time-varying delays. J. Appl. Math. Comput. 70, 1813–1835 (2024). https://doi.org/10.1007/s12190-024-02031-5

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