A new exponentially stable sliding mode control approach for a class of uncertain discrete systems with time delay

The exponentially stable sliding mode control problem for a class of uncertain discrete-time systems with delay is considered in this paper. A new sufficient condition is given to design the exponentially stable sliding mode surface. Based on the Lyapunov theory, a design strategy is then derived for the hitting controller. And all the conditions are expressed in terms of linear matrix inequalities. Finally, a numerical example is given to demonstrate the validity of the results.