Robust dissipativity and dissipation of a class of fractional‐order uncertain linear systems

作者：Liping Chen, Hao Yin, Ranchao Wu, Lisheng Yin, YangQuan Chen · 发表于：IET Control Theory and Applications · 年份：2019 · DOI：10.1049/iet-cta.2018.5745 · 被引用次数：35 · 研究领域：Advanced Control Systems Design、Neural Networks Stability and Synchronization、Stability and Control of Uncertain Systems

This study addresses robust QSR‐dissipativity and feedback dissipation of a class of fractional‐order (FO) uncertain linear systems. Both the state and controlled output matrices are with time‐varying norm‐bounded parameter uncertainties. Firstly, some new notions of QSR‐dissipativity and passivity for FO systems are introduced, the relationship between QSR‐dissipativity and asymptotic stability and input–output stability are discussed, respectively. Then, a sufficient condition in the form of linear matrix inequality (LMI) is proposed to ensure that such system is robustly QSR‐dissipative. According to this condition, a state feedback controller is proposed when the full states can be measured. Secondly, by employing LMI techniques and matrices singular value decomposition, sufficient conditions for the existence and a robust dissipation synthesis method are derived, respectively. Thirdly, a design method of dynamic output feedback controller is developed in order to guarantee that the closed‐loop system is dissipative. Finally, some numerical examples are provided to show the application of the proposed methods.