{"title":"状态相关切换下二维切换 T-S 模糊系统的稳定问题","authors":"","doi":"10.1016/j.jfranklin.2024.107192","DOIUrl":null,"url":null,"abstract":"<div><p>This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stabilization for 2-D switched T–S fuzzy systems under the state-dependent switching\",\"authors\":\"\",\"doi\":\"10.1016/j.jfranklin.2024.107192\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.</p></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0016003224006136\",\"RegionNum\":3,\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003224006136","RegionNum":3,"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}
Stabilization for 2-D switched T–S fuzzy systems under the state-dependent switching
This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.