MODEL-REDUCTION OF UNSTABLE SYSTEMS

A simple and powerful method for unstable model reduction has been dev eloped in which the approach is based on the fact that translation tra nsformations in the s-plane preserve the input-output properties of a system. Using translation transformations in the frequency domain it i s possible to change the stability of the system without losing input- output information. Although balancing requires that the model be asym ptotically stable, it reduces the model depending only on the informat ion of input to state and state to output. The stability requirement c omes from the computation of the controllability and observability gra mians 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 p ossible to use balancing to reduce the models of unstable systems by t ransforming them into the stable models, reducing the model order, and then transforming the models back. The method has been demonstrated b y case studies.