Study On Finite-time Stability And Control Of Fractional Differential Systems With Delay

Fractional calculus,as an arbitrary generalization of integral calculus on order,has been widely used in physics,chemistry,biology,engineering and other fields in recent years.In fact,many dynamic processes of practical systems are essentially fractional order.Moreover,singular and delay are commonly phenomena in practical systems.Therefore,we need to consider the impact of time delay and singular in order more accurately describe,analyze and apply the most practical systems.Recently,most scholars have considered the dynamic performance of a system within an infinite time interval,namely,the Lyapunov asymptotically stable of a different,ial system.Recently,most scholars have focused on the asymptotic stability of fractional differential systems,namely,the dynamic performance of the system in the infinite time interval.However,in practice,the transient performance of the system in the finite time interval is considered in most cases,namely,finite-time stability.Therefore,it is of great significance to study the controllability and finite-time stability problem of fractional-order differential systems with time delay and singular.The main research contents of this thesis can be divided into the following three aspects:Firstly,the relative controllability of a class of Caputo fractional-order neutral differential control systems with multiple delays in control is studied.A new expression of the system solution is obtained by Laplace transform.The necessary and sufficient conditions of relatively controllable are established by the Grammian matrix.Secondly,by using the generalized Gronwall inequality,the sufficient conditions for the finite-time stability of a class of nonlinear Caputo fractional-order neutral delay differential systems are given.Finally,the problem of finite-time stability and guaranteed cost control for a class of Riemann-Liouville fractional-order singular differential systems with time-varying delays and nonlinear perturbations is discussed.The sufficient conditions for the existence of feedback controllers for finite-time stability of fractional-order closed-loop systems are given by using Lyapunov direct method and combining linear matrix inequalities.An example is given to verify the validity of the results.