Stability Analysis For Stochastic Delayed Neural Network Of Neutral-type

Delayed neural networks of neutral-type are a kind of delayed nonlinear systems. These systems contain not only the influence of past states on present, but also the derivative of past states on present. Scholars both at home and aboard have paid attention to the theoretical and applied research results for neural networks of neutral-type in the past ten years, especially to the stability analysis for neural networks of neutral-type with time delays. However, in the applications and designs of neural networks of neutral-type, many uncertainties such as external perturbations, systematic errors, parameter fluctuations and data errors are unavoidable. Therefore, when modeling neural networks of neutral-type, unavoidable uncertainties should be taken into account. On the other hand, in many actual systems, such as electronic circuit systems, biological systems, chemical reaction process, stochastic disturbances are also unavoidable. The existence of stochastic disturbances factors could make delayed neural networks of neutral-type be instable. Therefore, when modeling neural networks of neutral-type, stochastic disturbances should be also taken into account. Activated by the above discussions, this dissertation deals with the problem of stability analysis for several stochastic delayed neural networks of neutral-type, including the robust stability of uncertain stochastic neural networks with time-varying delays; the global asymptotic stability analysis problem for uncertain stochastic neural networks of neutral-type with distributed delays; the delay-dependent robust stability analysis problem for uncertain stochastic neural networks of neutral-type with multiple discrete delays; the mean square stability analysis problem for uncertain stochastic BAM delayed neural networks of neutral-type; the stability analysis for a class of general stochastic neural networks of neutral-type with distributed delays. A series of stability conditions have been achieved in terms of linear matrix inequalities, and numerical examples are given to show the effectiveness of the obtained results. The main research contents of this dissertation can be summarized as follows:①By introducing a new Lyapunov-Krasovskill functional, sufficient criteria for the globally asymptotic stability of the uncertain stochastic neural network of neutral-type with time-varying delays are derived. These obtained criteria extend some existing ones. Numerical examples are provided to illustrate the applicability of the stability results.②Two types of uncertain stochastic neural network of neutral-type with discrete delays models are proposed and the stability of such models are investigated. First, the problem of global stability for a class of uncertain stochastic neural networks of nuetral-type with discrete and distributed delays is analyzed via It o? s formul and inequality method, some delay-dependent sufficient conditions are obtained, two illustrative examples are given to demonstrate the effectiveness of obtained results. Secondly, the problem of robust stability for uncertain stochastic neutral-type neural networks with mixed time-varying delays is considered, some new stability criteria are derived in terms of linear matrix inequality (LMI) by using the Lyapunov-Krasovskii functional approach, the linear matrix inequality (LMI) technique and the free-weighting matrix method, four numerical examples are presented to show the effectiveness of the obtained approach.③The delay-dependent asymptotic stability analysis problem for stochastic neural networks of neutral-type with multiple discrete and unbounded distributed delays is investigated. By using the Lyapunov-Krasovskii functional theorem, the method of inequality analysis and the linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to guarantee the global asymptotic stability in the mean square. In particular, the proposed stability conditions are derived in terms of LMI. The LMI can be easily solved by some standard numerical packages. In addition, two examples are given to show the effectiveness of the obtained results.④A class of stochastic BAM delayed neural networks of neutral-type with parameter uncertainties is considered. The neutral-type delays are assumed to be time-varying and the parameter uncertainties are assumed to be norm bounded. New global robust stability criteria are derived by utilizing the Lyapunov-Krasovskii functional and combing the method of inequality analysis. These criteria are obtained in the form of linear matrix inequality (LMI) and they can be easily checked. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results. Thus,it is of important significance to design the dynamic behaviors of the BAM neural networks of neutral-type.⑤The globally asymptotic stability analysis problem is considered for a class of general stochastic neural networks of neutral-type with time-varying delays. New stability analysis results are estabilisted based on a new Lyapunov-Krasovskii functional. It has been showed that the stability condition improves and generalizes some existing ones in the literature. Particularly, the stochastic perturbations terms are taken into account in the models. Therefore, the porpsoed results in this paper are more general than those reported in existing results. Meanwhile, the proposed model consists of stochastic perturbation, so these proposed criteria are universal and representative.