Approximate balanced-truncation model reduction for weakly coupled discrete-time systems

The computation of balanced-truncation reduced-order models of large-scale systems is impractical. However, for such complex systems there is typically a weak coupling between the subsystems. This is used here to derive approximate balanced-truncation reduced-order model of large-scale discrete-time systems with reliable and tractable computations. The condition for validity of the approximations and bounds on the norms of the approximation errors are also derived. These results are an extension, to the discrete-time case, of analogous results for continuous-time large-scale systems.