Stability Analysis About Several Kinds Of Stochastic Differential Functional

Stochastic differential equation stability analysis and controller design always is one of the most popular fields of the majority of scholars to research and discuss. Especially in recent years, there have been a lot of breakthroughs in stochastic differential equations which used in the fields of neural network system, financial system, ecosystem, social system and so on. This paper main discuss two types of stochastic systems, the one is analysis of stochastic BAM neural networks, the other is the design of the controller with Markov jumping system.Firstly, the exponential stability of a class of stochastic Cohen-Grossberg double associative memory neural networks with time varying delays is discussed. By constructing a suitable Lyapunov-Krasovskii functional, using stochastic stability theory and the freedom of matrix method, a sufficient condition for the globally exponentially stable in the mean square is gained. And comparison for the existing results, it can know our results greatly reduces conservative the considered system. Several numerical examples are given to verify the validity of the results. It is well known that the study of the stability of Markov jump systems is of great significance. Further, this paper study the global asymptotic stability for stochastic Cohen-Grossberg with Markov jump. The state trajectory of the system is given by a possible Markov transfer rate, which verifies the superiority of the conclusion.Secondly, for piecewise homogeneous Markov jump systems has the many author studied the neural network, but the research is not comprehensive, so the discussion of global asymptotic stability problem for piecewise homogeneous Markov bidirectional associative memory neural networks is necessary. This system contains discrete timevarying delay and distributed time-varying delays. Under the condition of a new assumption, the problem of the application of It?o s inequality is successfully solved. A new multiple Lyapunov-Krasovskii functional, and the sufficient conditions for the global asymptotic stability of the system are obtained.Thirdly, the singular stochastic Markov jump system H_∞control problem, the system is model dependent singular matrix Er(t). Through the design of a controller guarantees that the closed-loop system is stochastically admissible, and to meet the H_∞performance index γallowed. Based on stochastic Lyapunov functional, It?o stochastic analysis and linear matrix inequality approach, sufficient conditions for admissible index of the system are obtained. Analysis for the system H_∞performance index and design the controller.Finally, the robust reliable H_∞control for neural networks with mixed delays is discussed. In this system, It is inevitable to consider the sensors and actuators failure, which will affect the system stability and other performance. So people have to consider the safety and reliability of the system. According to the neural network system, we mainly discuss the actuators failure case of whether the system is stable and reliable is H_∞performance and other issues. Based on the linear matrix inequality and Lyapunov stability analysis, the sufficient conditions of the asymptotically stable in the mean square are derived for the closed-loop systems. According to the stability analysis, design the state feedback controller and by using the Matlab LMI toolbox obtain the H_∞gain matrix.