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.