Stability Analysis Of Recurrent Neural Networks With Time-Varying Delays Based On Quadratic Convex Techniques

The neural network model was established on 1940s and Hopfield neural network was proposed on 1980s, which have been widely concerned to until today. Along with the progression of scientific technology and the development of theoretical knowledge, recurrent neural networks have been applied to many fields, such as pattern recognition, image processing and so on. However, the influence of the network system performance and the external environment, the signal ususally appear a delay in the network transmission to interrupt a network. Therefore, it is a great significance to research into the stability of recurrent neural networks with time delays. On the basis of existing research results, this paper based on Lyapunov stability theory, convex technique and linear matrix inequalities (LMIs) were used to research into the stability problem of recurrent neural networks with time-varying delays, a new stability condition is presented.First of all, we researched into stability problem of recurrent neural networks with time-varying delays and disturbances, a new stability condition is presented. In order to extend the existing idea and further to reduce the conservative, this paper constructed a new Lyapunov-Krasovskii functional by using a quadratic convex technique to obtain a less conservative condition. Carried out by the Matlab simulation, verified the effectiveness of the proposed method.Secondly, based on the idea of the proof in the stability analysis of recurrent neural networks with single time-varying delays, this paper, we research a wider class of stability problem of recurrent neural networks with two additive time-varying delays by constructing a new Lyapunov-Krasovskii functional, combining a quadratic convex technique, reciprocally convex combination technique and convex polyhedron technique, respectively, the new stability condition is presented. Carried out by the Matlab simulation, verified the effectiveness of the proposed method.Finally, recurrent neural networks with two additive time-varying delays was applied to the practical engineering, firstly, a constructed time-varying delays model is established, an asymptotically stable condition of system is proposed by the experimental simulation to show that the result model is asymptotically stable.