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Robust stability and stabilization of fractional order linear systems with positive real uncertainty
Yingdong Ma1, Junguo Lu1, Weidong Chen1
1Department 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.
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.
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