分数阶线性系统的鲁棒稳定性与镇定及其正实不确定性。
Robust stability and stabilization of fractional order linear systems with positive real uncertainty.
机构信息
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.
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.
出版信息
ISA Trans. 2014 Mar;53(2):199-209. doi: 10.1016/j.isatra.2013.11.013. Epub 2013 Dec 14.
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.
本文研究了具有正实不确定性的分数阶线性系统的鲁棒稳定性和镇定问题。首先，给出了此类不确定分数阶系统渐近稳定的充分条件。其次，推导出了状态反馈控制器、静态输出反馈控制器和基于观测器的控制器存在条件和设计方法，以实现此类不确定分数阶系统的渐近稳定。所得结果以线性矩阵不等式的形式给出。最后，通过一些数值实例验证了所提出的理论结果。
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