Stability analysis and controller design for the performance improvement of disturbed nonlinear systems using adaptive global sliding mode control approach

This paper addresses a novel adaptive global nonlinear sliding surface for a class of disturbed nonlinear dynamical systems. A nonlinear gain function is used in the sliding surface to change the damping ratio and improve the transient performance of the controlled system. Initially, to get a quick response, a low value of damping ratio is obtained using a constant gain matrix. As the response of the system approaches to the origin, the damping ratio of the controlled system is improved and the overshoot and settling time of the closed-loop system are reduced. A novel control law without chattering is designed to satisfy the elimination of the reaching phase and achieve the presence of the sliding around the surface right from the beginning. Moreover, the adaptive tuning control law eliminates the necessity of the knowledge about the bounds of the external disturbances. Illustrative simulations on Genesio chaotic system with different values of the initial conditions and external disturbances are presented to show the robustness and success of the suggested design.