Finite Time Stability Of Fractional Order Differential Systems With Delay

Based on its good memory and genetic characteristics,fractional calculus has been applied in the fields of fluid mechanics,neural networks,intelligent control,and signal analysis and processing,and has attracted wide attention from scientists.With the development of science and technology,scientists continue to improve the theory of fractional calculus,which makes the fractional calculus get larger development.The stability is one of the most important theoretical foundations of fractional calculus systems and premise condition for the work of various systems.The stability of the system can be divided into asymptotic stability,Mittag-Leffler stability,finite time stability and so on.In the actual system,due to the influence of various factors,it is difficult to ensure the global stability of the system.How to ensure the system to meet the basic conditions of stable operation in finite time is an important topic in the study of finite time stability.In this paper,we will study the finite time stability for several different kinds of fractional differential systems.The main research contents of this paper can be split into the following chapters:In the first chapter,the development and significance of finite time stability of fractional differential systems are introduced.In the second chapter,some definitions and theorems of this paper are introduced.In the third chapter,the finite time stability problem of fractional order linear delay differential systems is researched.Through the method of Lyapunov function and linear matrix inequality(LMI),the criteria for the stability of fractional order delay differential systems in finite time are given.Then,by designing a feedback controller,the fractional order delay differential closed-loop systems can achieve finite time stabilization under the action of state feedback controller.Finally,specific numerical examples and system simulations are given to verify the feasibility of the theorem conditions in this paper.In the fourth chapter,the problem of finite time stabilization of fractional order singular delay differential systems with perturbation is researched.By constructing a new Lyapunov function,using LMI and generalized Gronwall inequality,sufficient conditions for the finite time stabilization of fractional order singular delay differential systems are provided.Under the function of the designed feedback controller,the system can be stabilized in finite time.Finally,specific numerical examples and system simulations are given to verify the feasibility of the theorem conditions in this paper.In the fifth chapter,the finite time stability and finite time boundedness of fractional order singular switched delayed differential systems are researched.By means of mean dwell time,Lyapunov function and LMI,the sufficient conditions for the finite time stability of the system are obtained.Then,under the condition of disturbance,the same method is used to obtain the bounded condition of the system in finite time.Numerical examples and system simulation are given to verify the feasibility of the theorem.