Research On The Chaos Synchronization Control Application Theory

This paper made a deep and full research on synchronization of chaotic systems,and got following new results.First, we discussed two kinds of Generalized Observers .After rigorous theoretic analysis, Generalized Observers of two kinds of chaotic system are put forward. After strictly theoretic proof, the feasibility of both Generalized Observers can be got at any dimensions. At the same time, we point out,a feedback synchronization controller can be got with the Generalized Observers. The method only need settle a pure algebra problem. Illustrations are also presented to show these conclusions are very effective.Second, we discussed a kind of chaotic completely couple-synchronization problem on basis of 1. In order to reduce coupled error, and to make the coupled process more easy, a complete direct synchronization method for coupled system is brought out. This method need not handled the coupled error in linear method, also need not know the state variable range of driving system. The coupled function constructed is only connected with driving system,the coupled parameter can be decided with Routh criterion. Experiments for Lorenz system demonstrate the effectiveness of this method. And whenever the stability's criterion of linear constant coefficient system or linear tome-varying continuous systems is employed, the error system should be handled in linear method, thus complete synchronization for coupled chaotic system becomes more difficult. Number simulations also explain realizing complete synchronization for coupled chaotic system not only with coupled method, but also with the coupled function.Third, On the basis of discriminative method of stability's in linear time-varying continuous systems, a high-to low-dimension feedback synchronization method is put forward for 3-D continuous chaotic systems. Main ideal of this method is that a kind of V function whose differential is not continuous is applied, combined the comparable principle, the stability discrimination of high dimensional linear time-varying continuous system can change into the stability discrimination of low dimensional linear time-varying continuous system. The method can divided into two main steps: First, the range of the state variables is determined by the numerical experiments; Second, the state variable feedback function and feedback gain can be got by the linear error system which can satisfy the eigenvalue of the Jacobian matrix is always nonpositive with time...