Robust stability and stabilization of continuous-discrete fractional-order 2D Fornasini–Marchesini second model with interval uncertainties

IF 2.7 4区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Asian Journal of Control Pub Date : 2024-04-17 DOI:10.1002/asjc.3380

Zhen Zhu, Jun-Guo Lu

{"title":"Robust stability and stabilization of continuous-discrete fractional-order 2D Fornasini–Marchesini second model with interval uncertainties","authors":"Zhen Zhu, Jun-Guo Lu","doi":"10.1002/asjc.3380","DOIUrl":null,"url":null,"abstract":"<p>This paper investigates the robust stability and stabilization problems of continuous-discrete fractional-order two-dimensional Fornasini–Marchesini second model with interval uncertainties. Firstly, for the nominal model with fractional-order \n<span></span><math>\n <semantics>\n <mrow>\n <mi>α</mi>\n <mo>∈</mo>\n <mo>(</mo>\n <mn>0,2</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\alpha \\in \\left(0,2\\right) $$</annotation>\n </semantics></math>, the unified LMI-based stability conditions are presented by general description of stable root-clustering sets. Secondly, these stability conditions are transformed to be more tractable for stabilization, and the LMI/BMI-based stabilization conditions are established via state feedback controllers. Meanwhile, one algorithm is proposed to solve the BMI-based conditions. Thirdly, facing interval uncertainties in this model, the LMI-based robust stability conditions and LMI/BMI-based robust stabilization conditions are established. Lastly, two examples are given to show the validity of our robust stability and stabilization results.</p>","PeriodicalId":55453,"journal":{"name":"Asian Journal of Control","volume":"26 6","pages":"3054-3066"},"PeriodicalIF":2.7000,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Control","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asjc.3380","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

Abstract

This paper investigates the robust stability and stabilization problems of continuous-discrete fractional-order two-dimensional Fornasini–Marchesini second model with interval uncertainties. Firstly, for the nominal model with fractional-order $α \in (0,2)$ , the unified LMI-based stability conditions are presented by general description of stable root-clustering sets. Secondly, these stability conditions are transformed to be more tractable for stabilization, and the LMI/BMI-based stabilization conditions are established via state feedback controllers. Meanwhile, one algorithm is proposed to solve the BMI-based conditions. Thirdly, facing interval uncertainties in this model, the LMI-based robust stability conditions and LMI/BMI-based robust stabilization conditions are established. Lastly, two examples are given to show the validity of our robust stability and stabilization results.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

具有区间不确定性的连续-离散分数阶二维 Fornasini-Marchesini 第二模型的鲁棒稳定性和稳定性

本文研究了具有区间不确定性的连续-离散分数阶二维 Fornasini-Marchesini 第二模型的鲁棒稳定性和稳定问题。首先，针对具有分数阶的名义模型，通过对稳定根簇集的一般描述，提出了基于 LMI 的统一稳定性条件。其次，将这些稳定条件转化为更易稳定的条件，并通过状态反馈控制器建立基于 LMI/BMI 的稳定条件。同时，提出了一种算法来求解基于 BMI 的条件。第三，面对该模型的区间不确定性，建立了基于 LMI 的鲁棒稳定条件和基于 LMI/BMI 的鲁棒稳定条件。最后，给出了两个示例来说明我们的鲁棒稳定性和稳定性结果的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Asian Journal of Control 工程技术-自动化与控制系统

CiteScore

4.80

自引率

25.00%

发文量

253

审稿时长

7.2 months

期刊介绍： The Asian Journal of Control, an Asian Control Association (ACA) and Chinese Automatic Control Society (CACS) affiliated journal, is the first international journal originating from the Asia Pacific region. The Asian Journal of Control publishes papers on original theoretical and practical research and developments in the areas of control, involving all facets of control theory and its application. Published six times a year, the Journal aims to be a key platform for control communities throughout the world. The Journal provides a forum where control researchers and practitioners can exchange knowledge and experiences on the latest advances in the control areas, and plays an educational role for students and experienced researchers in other disciplines interested in this continually growing field. The scope of the journal is extensive. Topics include: The theory and design of control systems and components, encompassing: Robust and distributed control using geometric, optimal, stochastic and nonlinear methods Game theory and state estimation Adaptive control, including neural networks, learning, parameter estimation and system fault detection Artificial intelligence, fuzzy and expert systems Hierarchical and man-machine systems All parts of systems engineering which consider the reliability of components and systems Emerging application areas, such as: Robotics Mechatronics Computers for computer-aided design, manufacturing, and control of various industrial processes Space vehicles and aircraft, ships, and traffic Biomedical systems National economies Power systems Agriculture Natural resources.

期刊最新文献

Issue Information Issue Information Issue Information Issue Information Adaptive output feedback time-varying formation tracking of multi-agent system with a leader of unknown input