Stability Analysis Of A Class Of Systems With Two Additive Time-varying Delays

With the development and cross penetration of communication technology,computer network and control science,the structures of control systems are becoming more and more complex,and the spatial distributions are becoming more and more extensive.Delay and randomness are important factors that cause instability of NCS.Therefore,it is of great significance to study the system with TADs and the neutral neural network system with TADs and Markov jump parameter.In this thesis,Lyapunov stability theory,stochastic theory,LMIs and so on are used to study the stability problems of the system with TADs and the neutral neural network system with TADs and Markov jump parameter.The main works are summarized as follows:1.The stability problem of the system with TADs is studied: Firstly,through the dynamic time delay decomposition method,the variation interval of dynamic time delay is divided into two unequal subintervals,and the suitable L-K functionals are constructed on these different subintervals.Secondly,the integral inequality and reciprocal convex method are used to estimate the derivative of the constructed L-K functionals,and several stability criteria of system with TADs are given in terms of LMIs.Compared with the existing criteria,the proposed criteria are less conservative and have lower numerical complexity.Finally,with the help of a typical system with TADs,the results are simulated by MATLAB.The results show that the upper bound of time delays obtained by the criteria in this thesis are significantly improved compared with related literature.2.For the neutral neural network system with TADs and Markov jump parameter:Firstly,the suitable random L-K functionals are constructed.Different from other literature,the characteristics of various time-varying delays and Markov jump parameters of the system are fully considered in the constructed L-K functionals.Secondly,the stability criteria in terms of LMIs are obtained by utilizing Jensen’s inequality and reciprocal convex method.Finally,a numerical example is given to verify the validity and advancement of the criteria.The results show that the upper bound of time delays obtained by the criteria in this thesis are significantly improved compared with related literature.