H∞ controller design for Nabla discrete fractional-order systems

IF 6.3 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

ISA transactions Pub Date : 2025-04-01 DOI:10.1016/j.isatra.2025.02.005

Jin-Xi Zhang , Yuanda Lv , Xuefeng Zhang , Witold Pedrycz

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引用次数: 0

Abstract

This article aims to provide several criteria with sufficient conditions for Nabla discrete fractional-order systems to satisfy a certain

H_{\infty}

performance index. Firstly, the instability region is approximated by a series of union sets of fan-shaped domains, and the mathematical expression of each fan-shaped domain is given. Secondly, by using the above approximation method and the generalized Kalman-Yakubovič-Popov lemma, some criteria with linear matrix inequality (LMI) formulations for the boundedness of the

H_{\infty}

norm of the transfer function matrix for Nabla discrete FOSs are derived. Thirdly, an LMI-based

H_{\infty}

state feedback controller design method is provided by using the projection lemma, which is aimed to stabilize the system and optimize its

H_{\infty}

performance index simultaneously. Finally, the effectiveness of the proposed approach is verified by the accurate numerical solutions and system state responses obtained from two simulation examples.

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离散分数阶系统的H∞控制器设计。

本文旨在为Nabla离散分数阶系统提供满足某H∞性能指标的若干充分条件判据。首先，用一系列扇形区域的并集逼近不稳定区域，并给出每个扇形区域的数学表达式；其次，利用上述近似方法和广义kalman - yakubovi - popov引理，导出了具有线性矩阵不等式（LMI）形式的Nabla离散FOSs传递函数矩阵H∞范数有界性的判据。第三，利用投影引理提出了一种基于lmi的H∞状态反馈控制器设计方法，以稳定系统并同时优化其H∞性能指标。最后，通过两个仿真算例的精确数值解和系统状态响应验证了所提方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ISA transactions 工程技术-工程：综合

CiteScore

11.70

自引率

12.30%

发文量

824

审稿时长

4.4 months

期刊介绍： ISA Transactions serves as a platform for showcasing advancements in measurement and automation, catering to both industrial practitioners and applied researchers. It covers a wide array of topics within measurement, including sensors, signal processing, data analysis, and fault detection, supported by techniques such as artificial intelligence and communication systems. Automation topics encompass control strategies, modelling, system reliability, and maintenance, alongside optimization and human-machine interaction. The journal targets research and development professionals in control systems, process instrumentation, and automation from academia and industry.