A new discrete-time sliding mode controller for nonlinear uncertain systems

This paper introduces a new algorithm for sliding mode control to stabilize a class of discrete-time nonlinear systems in the presence of uncertainties and external disturbances. The control algorithm is derived to guarantees the existing of quasi-sliding mode taking into accounts the upper bounds of uncertainties. As for the system stability, it can be found that the system is stabilized and finally restricted to a known region under the framework of sliding mode. This control scheme ensures robustness against parametric uncertainties and disturbances as well as chattering elimination. In the paper, after a detailed formalization of the proposed control algorithm, a numerical example for an inverted pendulum is considered, proving the effectiveness of the control methodology.