Research On Stability And Reachable Set Of Several Kinds Of Functional Differential Equations

The dynamic system has been studied by many scholars,due to its wide application in natural science and engineering technology.And lots of excellent research results have been reported,such as the stability analysis,filtering design problem,the reachable set estimation of dynamics system,and so on.In this paper,we study the following problems: the stability of the neural networks and the reachable set of linear systems.We make some beneficial research on the above problems,and the main achievements of this paper are as follows.1.The bound of reachable set for linear systems with discrete and distributed delays is studied in this paper.By utilising Lyapunov stability theory,delay decomposition technique,reciprocally convex method and free-weighting matrix method,a new ellipsoid bound of reachable set in the form of linear matrix inequalities is derived.Triple integrals are introduced in Lyapunov functional to study bound of reachable set for linear systems with discrete and distributed delays,which may lead to less conservative.2.Based on Lyapunov stability theory,delay decomposition technique,reciprocally convex method and free-weighting matrix method,bound of the reachable set for linear uncertain polytopic systems with disturbance and time-varying delays have been studied.A new ellipsoid bound of reachable set in the form of linear matrix inequalities is obtained.The proposed Lyapunov functionals contain triple integral terms and freeweighting matrices,which lead to less conservative.Tighter ellipsoidal bounding of the reachable set are obtained.3.This paper is concerned with bound of reachable sets for neutral delay linear systems with bounded peak disturbances,via delay decomposition method and freeweighting matrix method,constructing new Lyapunov functional.The proposed Lyapunov functional can lead to less conservative and tighter ellipsoidal bounding of the reachable set.Numerical examples show its validity.4.This paper investigates the problem of the globally exponential stability of neural networks with discrete and distributed delays through constructing new Lyapunov functional.A globally exponential stability criterion of neural networks is derived and it is expressed in the form of matrix norm inequality.The proposed result can not only guarantee the existence and uniqueness of the equilibrium point of the system,but also can be used to judge the stability of the system.Meanwhile,this paper focused on the exponential stability of interval neural networks with discrete and distributed time-varying delays,based on Lyapunov stability theory,Homomorphic mapping theory and M-matrix theory.A new delay-dependent stability condition of neural networks is given in the form of matrix norm inequality.The result decrease the conservativeness of dynamic system,and the constraint on discrete delay is relaxed,too.The stability condition is simple and can be verified easily,compared with the linear matrix inequality stability conditions.Numerical examples show its superiority.