Fixed time stability of a class of chaotic systems with disturbances by using sliding mode control. (December 2021) - Su, Haipeng; Luo, Runzi; Fu, Jiaojiao; Huang, Meichun
Abstract: 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. Highlights: This article investigates the fixed time stability of a class of chaotic systems with disturbances. A novel fixed time stability theorem is established based on the Lyapunov stability theory. Some novel controllers are designed to stabilize the chaotic system by using the sliding mode control technique. The control scheme is robust against the effects of the perturbations. The upper bound of convergence time is fixed which is determined by the control parameters regardless of initial conditions.