Fixed time stability of a class of chaotic systems with disturbances by using sliding mode control.

The main goal of this article is to consider the fixed time control problem of perturbed chaotic systems by virtue of sliding mode control. For this aim, this article presents a novel fixed time stability theorem at first by the Lyapunov tools. Then combining the obtained stability theorem and sliding mode technique, a new sliding mode surface is constructed and some novel controllers are designed appropriately to stabilize the discussed chaotic system. The proposed controllers have two main advantages: (1) The control criteria is robust against the effects of perturbations. (2) The convergence time, which is only dependent on the control parameters regardless of the initial conditions, is bounded by a fixed constant. Finally two typical systems are taken as the numerical examples to verify the validity of the control strategy.

The equal combination synchronization of a class of chaotic systems with discontinuous output.

This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.