Stabilisation Of Distributed-order Nonlinear System Based On Event-triggered Mechanism

Distributed-order calculus is a generalization of fractional-order calculus.It not only has the advantages that fractional-order calculus can describe the memorability and heritability of the system,but also retains the non-local characteristics of constant fractional-order calculus and allows the existence of multiple coexisting stages.It has been widely used in the fields of physics,biology and economics.Since event-triggered mechanism can effectively save communication energy on the premise of ensuring system control performance it has become an important control method for nonlinear system stability.The stability control of fractionalorder nonlinear systems based on event-triggered mechanism mainly focuses on the constant fractional-order nonlinear systems,but hardly considers the distributedorder nonlinear systems.In view of this,this thesis aims to study the stability of distributed-order nonlinear systems based on event-triggered mechanism.The main content of this thesis includes the following two aspects:1.Asymptotic stability of distributed-order nonlinear systems based on eventtriggered mechanismBased on the event-triggered sampling data control method,the asymptotic stability of a class of distributed-order nonlinear systems is studied.By designing the event-triggered sampling data controller and event-triggered strategy,and using the theory of distributed-order calculus,Lyapunov stability principle and matrix inequality technique,the sufficient conditions for the asymptotic stability of distributed-order nonlinear systems are established,and the calculation method of control gain matrix is given.Further,a guideline is provided to exclude Zeno behavior from the event-triggered policy.Finally,a numerical simulation example is given to verify the validity of the obtained criterion.2.Robust Stability of distributed-order nonlinear systems with uncertain parameters based on event-triggered mechanismBased on the event-triggered sampling data control method,the stability problem of a class of distributed-order nonlinear systems with uncertain parameters is studied.By designing the event-triggered sampling data controller and eventtriggered strategy,and using the theory of distributed order calculus,matrix eigenvalue theory,Lyapunov stability principle and matrix inequality technique,the sufficient conditions of robust stability of distributed-order nonlinear systems with uncertain parameters are established,and the calculation method of gain matrix is given.Further,a guideline is provided to exclude Zeno behavior from the event-triggered policy.Finally,a numerical simulation example is given to verify the validity of the obtained criterion.