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

Abstract

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.