The Research On Exponential State Estimation For Two Classes Of Jumping Neural Networks With Delay

With the rapid development of artificial intelligence,artificial neural networks have been widely studied and applied,such as image recognition,signal processing,parallel computing,and so on,since the 1940 s.Markovian jump is a kind of important random uncertain phenomenon.According to the characteristics of the mode transfer rate,it can be divided into a time-invariant Markov process and a time-variant Markov process(also known as a semi-Markov process).In this thesis,by introducing these two kinds of Markov jump ideas and considering the unavoidable delay in the actual system,the delayed neural network models with two classes of jumping are proposed,and the exponential state estimation of the two types of models is studied,respectively,which main content is divided into the following parts:1.A novel integral inequality is studied.Combining the idea of free-weight matrices and inequality operation skills,the novel free-matrix exponential-type integral inequality is proposed to improve the existing exponential integral inequalities.2.Using the new integral inequality,the exponential state estimation problem of delayed neural networks with Markov jumping is studied.According to the characteristics of Markov jumping neural networks with delay,based on continuous state feedback control and sampled-data control,respectively,combined with the proposed new integral inequality,the Lyapunov-Krasovskii functional with time delay is constructed,and the exponential stability criterion of the error system is established,and the effective state estimator is obtained.3.The problem of exponential state estimation for memristor-based neural networks with semi-Markov jumping and delay is studied.Firstly,to improve the effective utilization of network communication resources,a state estimator of sampled-data-based eventtriggered control is designed.Secondly,combined with the proposed new integral inequality,a delay-dependent Lyapunov-Krasovskii functional is constructed to establish the exponential stability criterion of the error system.Finally,the effectiveness and superiority of the proposed methods are verified by numerical examples.