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

  • Nguyen Huu Sau,
  • Tran Nguyen Binh,
  • Nguyen Truong Thanh,
  • Mai Viet Thuan

摘要

The primary focus of this paper is to investigate the \(H_{\infty }\) H state feedback control problem within uncertain fractional-order systems characterized by time-varying delays. Our approach centers on the development of an event-triggered \(H_{\infty }\) H 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 \(H_{\infty }\) H 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.