Research On Stability For Neural Networks With Mixed Delays And Application In Power System

Neural network, as a kind of typical nonlinear dynamic system, has caught people’s great attention because of its extremely rich dynamic characteristic. It is well known that, time delays are commonly encountered in real systems, and their existences are frequently the source of instability and poor performance. The effects of time delays, in particular distributed delay, must be taken into account in the description of neural network’s status. Namely, the development trend of neural network is related either at present or in history, and the networks are called neural networks with mixed delays. Recently, the dynamical behaviors of neural networks with mixed delays have been extensively studied by academics because of their applications in many areas such as pattern recognition, associative memory, and combinatorial optimization and so on. Among them, Lagrange stability, as an important branch of research, has also attracted worldwide attention in recent and achieved some theoretical results. In this paper, on the basis of predecessors’ research works, we further study systematically the dynamic behaviors of three kinds of mixed delayed neural networks, and mainly include that the existence and Rn+-tability for nonnegative equilibrium point of mixed delayed Cohen-Grossberg neural networks, Lagrange stability, global robust stability and globally exponentially attractive set of mixed delayed recurrent neural networks etc. What’s more, we apply the result of Lagrange stability for recurrent neural networks with time-varying and infinite distributed delays to power system, which is used to judging the Lagrange stability for power system. The main work and research results of this dissertation can be briefly described as follows:The existence and uniqueness of the nonnegative equilibria in the nonlinear complementary problem (NCP) for Cohen-Grossberg neural networks (CGNNs) with both time-varying and finite distributed delays are investigated. Based on the linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived guaranteeing the Rn+-global asymptotic stability of mixed delayed Cohen-Grossberg neural networks with nonnegative equilibrium in the first orthant. Moreover, when the equilibrium is positive, it can also be guranteed the Rn+-globally exponentially stable. The result extends the existing conclusion with literature and a numerical example is presented to indicate the viability of the theoretical analysis.The global exponential stability in Lagrange sense is further discussed for CGNNs with both time-varying and finite distributed delays. Under the premise of releasing the limitation on the activation functions being bounded, monotonous and differentiable, by virture of Lyapunov functional and Halanay delay differential inequality, several new criteria in LMIs form for global exponential stability in Lagrange sense of CGNNs are obtained. Meanwhile, detailed estimations of the globally exponentially attractive set are given out. The results include and improve some previous work and it is also verified that outside the globally exponentially attractive set, there is no equilibrium state, periodic state, almost periodic state, and chaos attractor of the CGNNs.The positive invariant and globally exponentially attractive sets for recurrent neural networks (RNNs) with both time-varying and infinity distributed delays are studied. Based on the general activation functions and by employing a new differential inequality and constructing Lyapunov functional and LMIs approach, several estimations for positive invariant and globally exponentially attractive sets are derived. Compared with the previous methods, these findings are less conservative, and two numerical examples are provided to illustrate this point.The global robust exponential dissipativity problem for interval recurrent neural networks (IRNNs) with both time-varying and infinity distributed delays is concerned. By means of the previous new differential inequality, constructed two different kinds of Lyapunov functions and made used of LMIs approach, several sufficient conditions are estabilished to guarantee the global robust exponential dissipativity for the addressed IRNNs. A numerical example is provided to demonstrate more general of the proposed results by compared with previous works.The method of chaotic analysis and LMI technique are used to determine Lagrange stability of power systems, respectively. The former mainly makes use of phase space reconstruction method to calculate maximum Lyapunov index λ1of time series for power system, and can judge Lagrange stability of power systems by the magnitude of λ1and the phase diagram of system. The latter puts forward the concept of Lagrange stability for power system based on analyzing the peoriodic quality of power system singal and the stability analysis method of nonlinear system. At the same time, by applying the previous criterion of Lagrange stability for power system to power grid based on the external observer, the method steps for determing Lagrange stability of power system are obtained. Moreover, the corresponding stability region can be found out, and it provides theoretical reference for further research Lagrange stability of power system.