Stability Control Problems For Two Classes Of Fractional Order Systems

Fractional order differential systems can more accurately describe the dynamic be-havior of complex systems than integer order differential systems,and fractional order systems have been widely applied in many fields,receiving a lot of research in recent years,including stability analysis and dynamic control.Stability is the prerequisite for the normal operation of the system.Stability is a very important and critical problem for the control system including fractional order system.So it is necessary to study the stability of fractional order system in depth.The stability control for two classes of fractional order systems is studied in this paper.Firstly,the research background and status of the stability for asynchronous switched sys-tems,singular time-delay systems and fractional order systems are introduced.Secondly,the exponential stability and finite-time stability of the asynchronous fractional switched system are analyzed respectively.Based on the average dwell time method,the sufficient conditions of system stability are obtained.By designing the state feedback controller and the observer-based state feedback controller,the closed-loop system is stable.Thirdly,the robust H_∞state feedback stabilization problem of singular fractional time delay systems is analyzed.By selecting appropriate Lyapunov function and using linear matrix inequal-ity method,the sufficient conditions for the stability of the system are given.Design a state feedback controller and an observer-based state feedback controller to stabilize the closed-loop system and validate the feasibility of the theorem through numerical examples.Finally,the thesis is summarized.