Model reduction of unstable systems

Abstract

A simple and powerful method for unstable model reduction has been developed in which the approach is based on the fact that translation transformations in the s-plane preserve the input-output properties of a system. Using translation transformations in the frequency domain it is possible to change the stability of the system without losing input-output information. Although balancing requires that the model be asymptotically stable, it reduces the model depending only on the information of input to state and state to output. The stability requirement comes from the computation of the controllability and observability gramians which are used for characterizing the contribution of the states to the input-output map. It has been shown in this paper that it is possible to use balancing to reduce the models of unstable systems by transforming them into the stable models, reducing the model order, and then transforming the models back. The method has been demonstrated by case studies.