Control of discrete-time nonlinear singularly perturbed system with uncertainty

We consider the controller design for the discrete-time nonlinear singularly perturbed system with uncertainty. The discrete-time singularly perturbed system with uncertainty is analyzed by the slow subsystem and the fast subsystem. From the uncertainty, the controller requires the contraction mapping condition for the existence of the manifold for the separation of two subsystems. Then, we design the composite controller for the stability of the slow subsystem and the fast subsystem. By the two subsystem´s stabilities, we show that the whole singularly perturbed discrete system with uncertainty is exponentially stable. Finally, we give an example to demonstrate our proposed result.