Admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties

IF 2.4 4区计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS

International Journal of General Systems Pub Date : 2023-06-25 DOI:10.1080/03081079.2023.2223755

Qing‐Hao Zhang, Jun‐Guo Lu

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引用次数: 2

Abstract

ABSTRACT This paper investigates the admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties. Firstly, based on the analysis of the regularity, causality and stability, novel admissibility conditions for nominal fractional-order singular discrete systems are derived including a necessary and sufficient condition in terms of spectral radius and a sufficient condition in terms of non-strict linear matrix inequalities. In order to eliminate the coupling terms and propose strict linear matrix inequality results, another novel admissibility condition is obtained, which is more tractable and reliable with the available linear matrix inequality software solver and more suitable for the controller design compared with the existing results. Secondly, the state feedback controller synthesis for the fractional-order singular discrete systems with interval uncertainties is addressed and the state feedback controller is designed. Finally, the efficiency of the proposed method is demonstrated by two numerical simulation examples.

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具有区间不确定性的分数阶奇异离散系统的容许性与鲁棒镇定

研究了具有区间不确定性的分数阶奇异离散系统的可容许性和鲁棒镇定性。首先，在分析分数阶奇异离散系统的正则性、因果性和稳定性的基础上，导出了分数阶奇异离散系统的新的可容许条件，包括谱半径的充要条件和非严格线性矩阵不等式的充要条件。为了消除耦合项并给出严格的线性矩阵不等式结果，得到了另一种新的容许条件，该条件与现有的线性矩阵不等式软件求解器相比更易于处理和可靠，也更适合控制器设计。其次，研究了具有区间不确定性的分数阶奇异离散系统的状态反馈控制器综合问题，并设计了状态反馈控制器。最后，通过两个数值仿真算例验证了所提方法的有效性。

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来源期刊

International Journal of General Systems 工程技术-计算机：理论方法

CiteScore

4.10

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： International Journal of General Systems is a periodical devoted primarily to the publication of original research contributions to system science, basic as well as applied. However, relevant survey articles, invited book reviews, bibliographies, and letters to the editor are also published. The principal aim of the journal is to promote original systems ideas (concepts, principles, methods, theoretical or experimental results, etc.) that are broadly applicable to various kinds of systems. The term “general system” in the name of the journal is intended to indicate this aim–the orientation to systems ideas that have a general applicability. Typical subject areas covered by the journal include: uncertainty and randomness; fuzziness and imprecision; information; complexity; inductive and deductive reasoning about systems; learning; systems analysis and design; and theoretical as well as experimental knowledge regarding various categories of systems. Submitted research must be well presented and must clearly state the contribution and novelty. Manuscripts dealing with particular kinds of systems which lack general applicability across a broad range of systems should be sent to journals specializing in the respective topics.