title: Robust stability and stabilization of fractional order linear systems with positive real uncertainty.
abstract: This paper investigates the robust stability and stabilization of fractional order linear systems with positive real uncertainty. Firstly, sufficient conditions for the asymptotical stability of such uncertain fractional order systems are presented. Secondly, the existence conditions and design methods of the state feedback controller, static output feedback controller and observer-based controller for asymptotically stabilizing such uncertain fractional order systems are derived. The results are obtained in terms of linear matrix inequalities. Finally, some numerical examples are given to validate the proposed theoretical results.
authors.affiliation: Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, No. 800 Dong Chuan Road, Min Hang, Shanghai 200240, P.R. China.
authors.forename: Yingdong
authors.initials: Y
authors.lastname: Ma
authors.affiliation: Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, No. 800 Dong Chuan Road, Min Hang, Shanghai 200240, P.R. China. Electronic address: jglu@sjtu.edu.cn.
authors.forename: Junguo
authors.initials: J
authors.lastname: Lu
authors.affiliation: Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, No. 800 Dong Chuan Road, Min Hang, Shanghai 200240, P.R. China.
authors.forename: Weidong
authors.initials: W
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004867:Equipment Design; D005246:Feedback; D017143:Fuzzy Logic; D016014:Linear Models; D017711:Nonlinear Dynamics; D035501:Uncertainty
keywords: Fractional order system; Linear matrix inequality (LMI); Positive real uncertainty; Robust stability; Robust stabilization