On the commutativity of decomposition and discretization for linear singularly perturbed systems

The commutativity of singular perturbation decomposition and multirate discretization of linear systems are analyzed. The authors give a decomposition technique for linear singularly perturbed systems with multirate piecewise-constant inputs, and prove its validity. Using this decomposition technique, the approximate slow and fast subsystems are then discretized in their natural time scales. These discrete-time subsystems are shown to be equivalent to those resulting from discretization followed by decomposition