Variable speed exponential control of a class of chaotic systems with external disturbances via sliding mode method

The problem of exponential control of a class of chaotic systems having external disturbances is addressed in this paper. By using a series of state variable transformations, the complicated n-order system is converted to a two-order system. With the second-order system obtained, a new non-singular fast sliding mode surface which makes the trajectories finite-timely converge to the origin is proposed. For realising the exponential control, a novel controller is presented to drive the states of the controlled system to the sliding surface. Unlike the previous literature, the convergence rate of the system can be adjusted by a specified parameter λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} in the controller. Besides, a new slide mode manifold which has no signal functions is designed, and both chatter phenomenon and singular problems occurring in the controller can be alleviated well. A chaotic system is applied to simulations to testify the validity of the presented approach.