Estimating the Globally Attractive Set and Positively Invariant Set of a New Lorenz-Like Chaotic System and Its Applications

This paper treats the globally exponentially attractive set and synchronization problem of a new Lorenz-like chaotic systems. Firstly, based on the definition of globally exponentially attractive set and Lyapunov stability theory, by constructing a family of generalized positive definite Lyapunov functions with radially unbound respect with to the parameters of the system, a new estimation of the globally exponentially attractive set of the new Lorenz-like chaotic system was obtained without existence assumptions and the results presented here improve the existing relative results on the globally exponentially attractive set as special cases and can lead to a series of new estimations. Secondly, nonlinear feedback control approach for two inputs with partial states is proposed to realize the globally exponential synchronization of two chaotic systems and some sufficient conditions for the globally exponential synchronization of two chaotic systems are obtained analytically. The controllers designed have simple structure and less conservation. The numerical simulation results show the effectiveness of the method.