Observer-based synchronization and parameter estimation of chaotic systems has been an interesting and important issue in theory and various fields of application. In this paper first we investigate the observer-based synchronization of a class of chaotic systems, and then discuss its parameter estimation via a single output. We assume that only the sum of the first and second state variables is available. By constructing a proper observer, some novel criteria for observer-based synchronization and parameter estimation are proposed via a scalar input. The Lü chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

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 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.