The general tracking problem for discrete-time dynamical systems

The general tracking problem for SISO nonlinear discrete-time systems is formulated, and includes both the asymptotic tracking problem and the exact tracking problems. Necessary and sufficient conditions for its solution are obtained. In the case where only input-output data is available, these conditions are characterized in terms of the system's nonlinear ARMA model. Conditions are also given for the existence of controllers to track periodic trajectories.