Stability Analysis Of Time-varying Delay Neural Network

When we study the neural network system, we often use some commonlymethods and techniques, for example: the linear matrix inequality technique, Lyapunovstability theory all are the basic skills. For the stability analysis of the stochastic neuralnetwork, stochastic analysis techniques also is a must to master. As well as, we alsoneed to use the inequality grading skills and some Lemmas to deal the inequalitiescleverly and reasonable and flexible use these basic skills to reduce the conservative ofthe conclusions of the paper.In this paper, I mainly discuss stabilities of two types neural networks. One is thestability determine of the time-varying delayed neural network, the other one is toanalyze the stability of stochastic neural networks with time-varying and distributeddelays. We got some conclusions of the stability and improved conditions. The mainresearch results are as follows:Firstly, I studied the neural networks systems with a single time delay underdifferent conditions. Secondly, I extended the time-varying delay to double to determinethe stability conclusions of the system. The two systerms considered the effects of thetime delay and its upper and lower bounds when determining the upper bpund of theLyapunov functions. but not just considered its time-varying delay lower bound of zero.The main innovation of this paper was that it discussed the two time delay systems butnot limited to one time delay systerm. According to different systems and therestrictions of them, I accurately structured the Lyapunov function, and took theadvantages of a variety of transformation techniques to reduce the conservative causedwhen enlarging processing the derivative of the Lyapunov function, and considered therelationship between the upper and lower bounds when estimating the upper bound ofLyapunov function, and taking into account the relative convex and convex polyhedronmethod and using linear matrix inequality technique and clever inequality zoomtechnology to reduce the stability of the conclusions conservative.Finally, I discussed the stability of associative memory stochastic neural networkswith time-varying and distributed delays.In this part, I considered the impact of time delay factors and random disturbance. I got the system’s global asymptotic stabilityconditions by constructing new Lyapunov function, based on Lyapunov stability theoryand linear matrix inequality, then under the help of LMI control tool software.