Dynamical Analysis And Control For Nonlinear Systems With Leakage Delay

As we all know when a dynamical system is exposed in some real environment, it will be affected by a lot of external factors. Time delays are generated due to some reasons such as the time taken in the transformation of signs between different parts of a system. Stochastic perturbation is another important factor affecting the dynamical systems. These factors are the sources to make the system become oscillating and not stable. Some delay differential equation models are made to describe the system in order to get some fine properties of the system. In the delay system, the change rate of the state depend not only on the present state but also the state of the past, even more on the change rate of the past. It is valuable to consider the analysis and control of the delay system. In this thesis we using the methods from Lyapunov stability theory of differential equations, linear matrix inequality, graph theory and stochastic differential equation to investigate the dynamical behaviors for the BAM model and GRN model with leakage delays. On the other hand, some control problem by using the sampled-data control strategy for the BAM model and GRN model with leakage delays are also studied here.The main points of the thesis are listed in detail as follows:1. We investigate the dynamical behaviors of the bi-directional associative memory(BAM) neural networks with sample-data input and delays in the leakage term of model. The so-called input-delay technique is use to obtain sufficient condition for the exponentially stability of the model. Due to the wide applications of continuously distributed delay in system models, we investigate the stability of BAM neural networks with a continuously distributed delay in the leakage term of the system model and sampled-data input. Numerical examples are provided to show the efficiency of the theoretical analysis.2. Analysis about the effect of the leakage delay is given, it shows that when the delays in the leakage term is zero or very small the system is stable, however, if the leakage delay pass some threshold, the system becomes not stable. We use the sampled-data control strategy to stabilize the BAM neural networks with leakage delays and obtained some sufficient conditions for the purpose. Then we also use the sampled-data control strategy to stabilize a GRN with leakage delays. Some sufficient conditions are obtained based on appropriate Lyapunov functionals. Numerical examples are used to show the efficiency of the methods proposed here.3. We investigate the stability of a neutral GRN with leakage delay, some sufficient conditions are obtained. The stability of a stochastic GRN with a Markovian switch and mixed delays is also studied. The results obtained here generalized corresponding results appeared in literatures. Numerical examples are used to show the efficiency of the theoretical results proposed here respectively.4. We investigate the problem of how to design a controller to stability a discrete linear system by using the observations. Here, the observation quantity is attacked by some external sources, it make this problem more realistic and difficult. In the first section,some sufficient condition for squared ultimate bounded of the solution is obtained. In the second section, we use the idea of the first section to get some sufficient condition for squared ultimate bounded consensus of the solution of a multi-agents system.Numerical examples are provided to show our theoretic analysis.