State Feedback And Impulsive Controls For Some New Chaotic Systems

Chaos is a common phenomenon in nonlinear systems.With the development of chaos theory,many new chaotic systems were designed by scholars.The control and synchronization of new chaotic systems are discussed in this paper by using feedback control,impulsive control,and adaptive control.The main contents are depicted as follows:In chapter 2,the robust stability of a new chaotic system with nonlinear perturbations is studied by employing impulsive control approach.When the parameters are known,sufficient conditions for robust synchronization are obtained.Moreover,the stability of the chaotic system with impulse time windows is also considered by using mathematical induction.Finally,finite-time synchronization of another new system with stochastic perturbations is investigated.In chapter 3,the robust stability of a new hyperchaotic system with uncertain distur-bances is studied by using time delayed impulsive control method.Sufficient conditions for global asymptotic stability are obtained.Modified projective synchronization of a new hyperchaotic system is studied by employing the impulsive control and feedback control method.It is easy to see by Theorem 5 that if the scaling factors ?1,?2,?3,?4 satisfy?12=1,?2 = O??1?3,then systems(3.2.2)and(3.2.5)will achieve modified projective syn-chronization without the feedback controller U.Finally,the stability of the hyperchaotic system with impulse time windows is investigated by using mathematical induction.In chapter 4,based on the Lyapunov stability theory,the anti-synchronization between a new chaotic system and the Lu chaotic system is studied by using feedback control method.By selecting an appropriate controller,the anti-synchronization between the chaotic system and the Chen chaotic system is realized.Finally,an adaptive controller and a feedback controller are designed to synchronize the two different hyperchaotic systems respectively.