Stability analysis and stabilisation of continuous-discrete fractional-order 2D Fornasini–Marchesini first model. Issue 2 (25th January 2023)

• Record Type: Journal Article
• Authors: Zhang, Jia-Rui; Lu, Jun-Guo; Zhu, Zhen
• Is Part Of: International journal of systems science. Volume 54:Issue 2(2023)
• Page Start: 333
• Page End: 344
• Publication Date: 2023-01-25
• Subjects: Continuous-discrete two-dimensional Fornasini–Marchesini first model -- structural stability -- Generalized–Kalman–Yakubovich–Popov Lemma -- fractional order -- stabilisation -- linear matrix inequality; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2022.2122901
• Languages: English
• ISSNs: 0020-7721

Abstract

Abstract : This paper focuses on the structural stability and stabilisation of the continuous-discrete fractional-order two-dimensional Fornasini-Marchesini first model. The sufficient and necessary stability conditions are given in polynomial form at first. Secondly, to make the problem solvable, based on the property of Kronecker product and the Generalized–Kalman–Yakubovich–Popov Lemma, the new sufficient and necessary stability conditions are established in the form of linear matrix inequalities. Thirdly, with the help of the Projection Lemma, the stabilisation conditions are obtained after introducing a state feedback controller, which can be solved with an iterative linear matrix inequality algorithm. In the end, the effectiveness of the proposed results is verified by two numerical examples.