Fractional-order System Stability Analysis Based On Event-triggered Mechanism

Considering the superiority that event-triggered mechanisms can reduce the number of control tasks,and improve the utilization efficiency of communication resources and so on,in this thesis,stability issues of several kinds of fractional-order systems are studied under the event-triggered control.Firstly,the asymptotic stability of a class of observer-based uncertain fractional-order systems is investigated.Secondly,the robust tracking control of the considered system is further studied.Then,the finite-time stability of a class of fractional-order singular systems is discussed.Finally,the transient stability analysis in a finite time interval for a class of fractional-order switched systems is given.The specific research content includes the following four aspects:Due to the difficulty of measuring full-dimensional state variables in practice,an observer-based asymptotic stability problem for a class of uncertain fractional-order systems is firstly studied.By designing an appropriate fractional-order observer,an event-triggered condition based on the observer state is constructed,then under the action of the designed feedback controller,a suficient condition for asymptotic stability of the corresponding fractional-order closed-loop system is given.Then,by means of Schur complement lemma,a feasible inequality condition is obtained,and the design methods of state feedback controller and observer gain matrix are given,respectively.Finally,the effectiveness and superiority of the theoretical part are verified by the comparison with the conventional periodic sampling controller.At the same time,the event-triggered tracking control of the uncertain fractionalorder system is further discussed.Firstly,the error between the system's output and the given reference signal is used to design the corresponding event-triggered strategy.Secondly,with the help of zero-order holder,the action period of each controller is determined according to the practical demand on the premise of ensuring the system's required stability performance.Then,under the action of the aperiodic feedback controller,a linear matrix inequality condition for asymptotic stability of the augmented tracking closed-loop system is presented,which means the asymptotic tracking goal is finally achieved.In addition,based on the event-triggered mechanism,finite-time stability of a class of fractional-order singular systems is studied.Different from the asymptotic stability in Lyapunov's sense,the transient behavior of a fractional-order singular system in a given finite time interval is studied in this thesis under the event-triggered control.Firstly,the regular and impulse-free properties of the considered system are proved.Then,by using the Lyapunov function,a sufficient condition of the finitetime stability for the studied system is derived.Finally,a numerical example is given to illustrate the feasibility of the theoretical approaches.Finally,the finite-time stability problem of the fractional-order switched system,which is regarded as a special class of hybrid systems,is considered in this thesis.Based on the theoretical analysis and numerical simulation for the fractional impulsive function and fractional piecewise-defined function,the essential and internal structure for the fractional-order switched system are reconsidered.In fact,it is proposed in this thesis that the property of the additivity of integration on intervals for integer-order integral does not hold for fractional integral,that is to say,t0Dt-?f(t)?t0Dt1-?f(t)+t1Dt-?f(t)for ??>0,t0