Time-scale separation of nonlinear singularly perturbed discrete systems

In this paper, we investigate the time-scale decomposition of the nonlinear singularly perturbed discrete system into lower-order subsystems; the slow subsystem and fast subsystems. In the singular perturbation method, the time-scale separation is inevitable for the analysis of the system stability and the composite control design. Using Tikhonov´s theorem, we obtain the slow subsystem and the fast subsystem separated from the nonlinear singularly perturbed discrete system. This time-scale separation method plays an important role in the stability analysis, composite control design of the nonlinear singularly perturbed discrete system.