Frequency limited model reduction techniques for discrete-time systems

The main drawback of pioneer frequency limited Gramians-based technique by Wang and Zilouchain for discrete time system is that it yields unstable reduced order models (ROMs) of stable original system. There exist some techniques in literature that produce stable ROMs, however, these techniques yield relatively large approximation error. In this brief, three modified techniques of model reduction for discrete time systems are being presented. These techniques preserve the stability in ROMs, mostly yield low approximation error (when compared to existing stability preserving techniques) and additionally contain frequency response error bounds. Several related examples are also illustrated. Comparison of results show the effectiveness of proposed techniques.