This paper presents a novel chattering free sliding mode control method for a class of nonlinear systems in the presence of matched disturbance and mismatched disturbance based on an extended state observer. First, a nonlinear extended state observer based on the hyperbolic tangent function is constructed to estimate the mismatched disturbance. And the second order extended state observer error system is proved to be bounded stable by using Lyapunov stability theory. Then a novel chattering free sliding mode surface integrated with the disturbance estimation is designed for this system even with mismatched disturbance. The theoretical analysis indicates that the system states can be stabilized to a neighborhood of the equilibrium point under the proposed controller. Compared with the traditional chattering free sliding mode control method, the presented control strategy can expose satisfactory control performance with chattering reduction and mismatched disturbance suppression. Finally, simulation results demonstrate the effectiveness of the proposed method.

The problem of adaptive robust control for uncertain nonlinear systems with time-varying delay is considered in this paper. The upper bound of the uncertainty is assumed to be nonlinear functions with unknown coefficients. By using adaptive control method, a class of adaptive robust state feedback controller is proposed. Based on Lyapunov-Krasovskii method and Lyapunov stability theory, it is shown that the controller designed can render the uniform asymptotic stability of the system. Finally, a numerical example is given to show the controller is valid.