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The purpose of this paper is to find a practical active sliding mode control approach for synchronization of two uncertain chaotic systems.

Sliding mode control approach is known to be an efficient alternative way to implement synchronization for uncertain chaotic systems. However, design of traditional sliding mode controller usually needs complex state transformation. Owing to a novel idea of virtual state feedback, a control strategy for synchronization of uncertain chaotic systems is presented, which does not need any complex state transformation. Furthermore, based on Lyapunov stability theory, a sufficient condition is drawn for the robust stability of the error dynamics of synchronization for uncertain chaotic systems.

A novel active sliding mode control approach is proposed to achieve the synchronization of two uncertain chaotic systems.

The main limitation is that uncertainties must meet matched conditions.

The paper presents a useful control approach for synchronization of two uncertain chaotic systems.

The proposed sliding mode control approach based on novel virtual state feedback does not need any complex state transformation, unlike the traditional sliding mode control.

The purpose of this paper is to find an appropriate sliding mode control strategy for neutral systems with time‐delays in the presence of unmatched parameter uncertainties and external disturbance.

Owing to the complexity of uncertain neutral time‐delay systems, some conclusions for system stability and stabilization are complicated non‐linear matrix inequality (NLMI). Through virtual state feedback control, a sliding mode controller is designed to guarantee state trajectories from any initial condition are attracted to the sliding mode plane in a finite time and remain there for all subsequent time, which can avoid the complicated NLMI. Furthermore, a delay‐independent sufficient condition for the design of robust stable sliding mode plane is obtained in term of LMI.

The sliding mode controller for uncertain neutral time‐delay systems is designed and a delay‐independent sufficient condition for the design of robust stable sliding mode plane is obtained.

The main limitations are that external disturbance must meet matched condition.

A useful control strategy for uncertain neutral systems with time‐delays.

The virtual state feedback control is designed so to avoid the complicated NLMI.

This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.

The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm.

The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics.

The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.