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In this paper, a class of three dimensional nonlinear chaotic dynamic systems, which have only one equilibrium position, are studied. The least conservative linear feedback control is introduced to make the systems globally exponentially stable. For four kinds of nonlinear chaotic systems, Sport D, I, J, L presented in reference [1], since the correlation of three equations in each system are good enough, it is relatively easy to realize linear feedback to achieve the aim of controlling chaos. Simulations are proposed to verify the good performance of the controlled systems with the given linear controllers.

In the paper, the globally stability for Genetic Regulator Networks with mixed time-delays is studied. By using derivative mean value theorem, two sufficient and necessary conditions for globally unformly asymptotic stability and global exponential stability of the trivial solutions of the GRNs with mixed time-delays are proposed. Finally, a simple example is given to demonstrate the correctness of the proposed results.

In this paper, we have discussed the full-order robust observer design problem for a class of nonlinear uncertain systems with time-varying delay. The goal of this problem is to design a nonlinear robust observer such that, for time-varying delay and unstructured parameter, the observer can guarantee the observing process robustly stable. A robust nonlinear observer is obtained, the observer gain matrix is included in a Hamiltonian matrix. A numerical example is given to demonstrate the validity of the proposed approach.