不确定奇异分数阶互联系统非脆弱分散H∞控制

doi:10.12068/j.issn.1005-3026.2023.02.001

东北大学学报（自然科学版） ›› 2023, Vol. 44 ›› Issue (2): 153-161.DOI: 10.12068/j.issn.1005-3026.2023.02.001

• 信息与控制 • 下一篇

不确定奇异分数阶互联系统非脆弱分散H_∞控制

杨冬梅，孙义兵

(东北大学理学院，辽宁沈阳110819)

修回日期:2021-12-13 接受日期:2021-12-13 发布日期:2023-02-27
通讯作者: 杨冬梅
作者简介:杨冬梅(1966-)，女，辽宁沈阳人，东北大学教授.
基金资助:
国家自然科学基金资助项目(61673100).

Non-fragile Decentralized H_∞Control for Uncertain Singular Fractional-Order Interconnected Systems

YANG Dong-mei， SUN Yi-bing

School of Sciences， Northeastern University， Shenyang 110819， China.

Revised:2021-12-13 Accepted:2021-12-13 Published:2023-02-27
Contact: SUN Yi-bing
About author:-
Supported by:
-

摘要/Abstract

摘要： 研究了阶次在0到1上的不确定奇异分数阶互联系统的非脆弱分散H_∞控制问题.对现有的奇异分数阶线性系统容许且满足H_∞性能的判定条件进行推广，以严格线性矩阵不等式的形式给出新的判定准则；通过对互联系统特殊结构的分析，利用线性矩阵不等式方法和矩阵分解技术，分别在加法和乘法控制器增益扰动下，给出非脆弱分散H_∞控制器存在的充分条件和设计方法.在控制器的设计过程中，对互联矩阵没有加以限定，得到严格的线性矩阵不等式判据，在一定程度上降低了系统的保守性.利用LMI工具箱及Simulink数值仿真验证了结论的有效性.

关键词: 分数阶;奇异互联系统;容许性;H_∞性能;非脆弱控制

Abstract: The non-fragile decentralized H_∞ control problems for uncertain singular fractional-order interconnected systems with commensurate order 0<α<1 are studied. The existing criteria for admissibility and H_∞ performance of singular fractional-order linear systems are extended. And the new criteria are given in the form of strict linear matrix inequality. Based on those conclusions， through analysis of the special structure of interconnected systems， under additive and multiplicative disturbances of controller gains， sufficient conditions for the existence of non-fragile decentralized H_∞ controllers and their design methods are given by using linear matrix inequalities and matrix decomposition technology. In the design process of controllers， the interconnected matrices are not limited and strict linear matrix inequality criteria are obtained， which reduce conservatism of the systems to a certain extent. The effectiveness of the proposed methods is verified by LMI toolbox and Simulink numerical simulation.

Key words: fractional-order; singular interconnected systems; admissibility; H_∞ performance; non-fragile control

中图分类号:

TP273

杨冬梅，孙义兵. 不确定奇异分数阶互联系统非脆弱分散H_∞控制[J]. 东北大学学报（自然科学版）, 2023, 44(2): 153-161.

YANG Dong-mei， SUN Yi-bing. Non-fragile Decentralized H_∞Control for Uncertain Singular Fractional-Order Interconnected Systems[J]. Journal of Northeastern University(Natural Science), 2023, 44(2): 153-161.

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不确定奇异分数阶互联系统非脆弱分散H_∞控制

Non-fragile Decentralized H_∞Control for Uncertain Singular Fractional-Order Interconnected Systems

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不确定奇异分数阶互联系统非脆弱分散H∞控制

Non-fragile Decentralized H∞Control for Uncertain Singular Fractional-Order Interconnected Systems

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不确定奇异分数阶互联系统非脆弱分散H_∞控制

Non-fragile Decentralized H_∞Control for Uncertain Singular Fractional-Order Interconnected Systems