Event‐triggered H∞ control for fractional‐order time‐delay systems

Abstract

This paper considers the problem of designing event‐triggered state feedback controllers for uncertain fractional‐order systems subject to time‐varying delays. An event‐triggered controller is proposed based on an event‐triggered mechanism and the refined fractional‐order Razumikhin theorem. This controller guarantees the uniformly asymptotic stability of the controlled system while maintaining a predefined performance index. The uniformly asymptotic stability of the controlled system is understood that the zero solution of the uncertain fractional‐order time‐delay systems without external disturbance is uniformly asymptotically stable. The main difficulty of this problem lies in the memory and heritability 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. The Zeno phenomenon exists when an infinite number of discrete transitions occur in a finite time interval. To overcome this difficulty, new event‐triggered state feedback controllers without Zeno behaviors are designed based on inequality techniques and several essential properties of fractional‐order calculus. Finally, the effectiveness and feasibility of the proposed method are demonstrated by a numerical example.