Input-to-state Stability For Stochastic Neural Networks With Time-Varying Delays

In recent years, more and more people realized the importance of the stability of stochastic neural network along with stochastic neural network widely used in optimization organization, signal processing, pattern recognition and artificial intelligence. As far as we know, the stability of stochastic neural networks have had many achievements. In practice, however, the control system often suffers from disturbances, such as some small changes of control, as well as errors exist in observation. Thus requiring control system not only to stabilize, but also control system requirements input-to-state stability. This article based on Lyapunov-Krasovskii functional, Ito formula and stochastic differential equations, we study the input-to-state stability of three typies delay of stochastic hopfield neural network. The main contents are as follows:First, it generally describes the research background, research status and significance of this issue, and gives the fundemental problems existing in the research. Then, it introduces Jensen inequality, Ito formula, Schur complement lemma, Linear matrix inequality, Lyapunov stability theory, the definition of input-to-state stability, stochastic input-to-state stability theorem and some common lemmas.Secondly, it gives the corresponding description of the problem which studied in this paper,and then builds a relevant stochastic delay hopfield neural network model, and discusses the stochastic input-to-state stability of time-varying delay model, multiple time-varying delays model and interval time-varying delays model. By constructing suitable SISS-Lyapunov-Krasovskii functional, and using Ito formula to process the stochastic differential equation model. We use Jensen inequality, Schur complement lemma, as well as several other important inequalities to analyze the derivation results, In the analysis, we make appropriate scaling for the derivative results of SISS-Lyapunov-Krasovaskii function, then obtain input-to-state stability conditions of the system, and give a sufficient input-to-state stability condition for stochastic neural network with delays in Linear Matrix Inequality (LMI) form. So that the problem of input-to-state stability of stochastic neural network is transformed into feasibility problem of linear matrix inequalities. Later, examples are given to verify the feasibility.Finally, we summarize and prospect the full text, point out the research results in this paper and the next research direction. This paper adopts the SISS-Lyapunov-Krasovaskii functions combining the basis of state variable quadratic and cross integral term. When we analysis the problem of input-to-state stability of system, fully take into account the stochastic term and various types of varying delays present in the system, the final result is obtained easier using MATLAB LMI toolbox to verify the feasibility of results, Simultaneously, LMI reduces the conservation of the result. Later, the graphic simulation also shows that the effectiveness of the stochastic input-to-state stability sufficient condition obtained in this paper.