Research On Performance Analysis And Estimation For A Few Types Of Delayed Neural Network Systems

In this thesis,the stability,passivity,dissipativity and state estimation problems of several classes of delayed Neural networks(NNs)are studied.First of all,this thesis takes the stability problem of delayed NNs system as the beginning and foundation,paving the way for the subsequent research on extended dissipativity.Subsequently,in view of a spe-cial case of dissipativity—passivity,the passive control problem of Markovian jump NNs is further discussed.Finally,this thesis studies the finite-time state estimation problem of semi-Markovian jump NNs.Based on the Lyapunov stability theory,combined with ma-trix analysis,stochastic process and other related knowledge,the improved stability and dissipativity criteria for system are proposed and numerical simulation analysis is used to verify the effectiveness and superiority of the proposed method.The specific content of this thesis can be summarized as follows:1.An improved stability criterion for discrete NNs with constant leakage time de-lay and discrete time-varying delay is proposed.Firstly,a new Lyapunov functional is constructed by adding multiple triple summations.Secondly,the difference terms of the Lyapunov functional are processed by the novel sum inequality and inverse convex com-bination technique.Then,through detailed analysis of different time-delay situations,an improved time-delay-related stability criterion is obtained.Finally,three numerical ex-amples verify the feasibility of the results.Compared with the existing literature,it can be found that this result effectively reduces the conservativeness of the system.2.The improved stability and extended dissipativity criteria for discrete time NNs with additive time-varying delays are proposed.Firstly,a new Lyapunov functional is constructed by adding multiple summations involving additive time-varying delays.Sec-ondly,by introducing more zero equations and using novel double summation inequali-ties,the difference terms of the Lyapunov functional are processed.Then,with the help of Finsler's lemma,the improved exponential stability and extended dissipativity criteria for the generalized NNs with additive time delays are obtained.And the extended dissi-pativity performance includes l₂-l_?,H_?performance,passivity,strict(Q,S,R)-?-dissipativity and strict(Q,S,R)-dissipativity.Finally,five numerical examples fully verify the feasibility of the obtained results.Moreover,compared with the existing liter-ature,it is not difficult to find that this result effectively reduces the conservativeness of the system.3.The passive control of Markovian jump discrete time NNs with incomplete tran-sition probability and unreliable channel is designed.We use the knowledge of stochastic process to analyze the lack of information related to the switching rule and the channel fading phenomena in the delayed system.Then,by designing a mode-dependent event-triggered controller,the event-triggered passivity criterion is obtained.Finally,one nu-merical simulation experiment verifies that this event-triggered mechanism effectively reduces the energy consumption of the system.4.The finite-time state estimation of semi-Markovian jump NNs with distributed leakage delay and linear fractional uncertainty is designed.First,the method of linear fractional uncertainties is used to deal with the uncertain parameters of the system and a full-order state estimator is designed.Then,more delay-related augmented Lyapunov functionals are constructed,and the latest integral inequalities and time-delay division method are used to deal with the derivation results of the augmented Lyapunov functionals.Thereby,we obtain the finite-time bounded criterion of the semi-Markovian jump state estimate system.Finally,the feasibility of the proposed method is verified by numerical examples.