Stability And Synchronization Analysis Of Time-Delay Neutral Network With Markovian Jumping

In practical applications such as the economic system,flight control system and robot operating system,the parameters and structure of the system may change abruptly due to component failures,external environment interference and interconnected subsystem coupling changes.In order to represent this phenomenon,hybrid dynamic systems are usually used for modeling.Markovian jump systems are usually used to represent such systems.The hopping system switches randomly from one mode to another.Therefore,it is significant to investigate stabilization of neutral network with Markovian jumping.In addition,the development of science and technology has promoted the progress in the fields of power,aviation,communications and manufacturing,which formed various large-scale and complex-structured systems.This kind of systems generally has the phenomenon of time delay and external interference,which leads to the degradation of systems performance and the deviation of the received measurement signal even of instability.Markovian jump and time delay usually occur in the practical application,so when modeling the actual dynamic system,Markovian jumping of neural network is usually used to study its dynamic characteristics.This thesis focuses on the neural network with time delays and Markovian jumping,Lyapunov-Krasovskii stability theory,generalized It(?) formulas,inequality analysis technique and Linear Matrix Inequalities method are used to obtain exponential stability conditions and adaptive synchronization conditions;Combined with Markovian jumping,semi-Markovian jumping and Markovian jumping with uncertain transition probabilities,the stability and synchronization of neural networks with various time delays are studyed.The above research work will enrich the stability and synchronization theory of neural network dynamical systems,and solve the key problems of the exponential stability and adaptive synchronization conditions of neural network with various time delays and Markovian jumping.The main researching contents and innovativeness of this thesis are as follows.(1)The problem of feedback controller designed to achieve adaptive synchronization is investigated for neural network with Markovian switching and Lévy process.Based on Lyapunov functional,It(?)s formula and inequality analysis technique,the goal is to obtain some criteria to ensure adaptive stabilization for the error system.Moreover,the update rate of the feedback controller is given,which ensures the adaptive synchronization of the response system and the drive system.Finally,a simulation example is offered to verify the effectiveness of the theoretical results.(2)The problem of exponential stability is investigated for neural network with semi-Markovian switching and leakage delay.The time delays of dynamical system are contained with leakage delay,distributed time delay,discrete delay and neutral-type delay.Leakage delay is widely present in the negative feedback of neural network,and it has a great influence on the dynamic behavior of neural network.In addition,the introduction of semi-Markovian jumping makes the neural network more extensive.through combinations of stability analysis method,Lyapunov-Krasovskii functional and inequality analysis technique,some sufficient conditions have been achieved to undertake the exponential stabilization of given neural network system.Finally,a simulation example is offered to verify the effectiveness of the theoretical results.(3)We study the exponential stability of a class of neutral delay neural networks with impulsive perturbations and Markov jumps whose transition probabilities are partially unknown.By using Lyapunov theory and impulsive theory,combined with inequality analysis techniques,we reduce the conservatism of the results and obtain sufficient conditions for the exponential stability of delay neural networks.Finally,a numerical example is given to demonstrate the effectiveness of the proposed method and the results.