Model reduction of singular systems

The model reduction problem for singular systems is investigated. Firstly, the model reduction algorithm reported in Perev and Shafai (1994) is presented and proved to be wrong. Detailed examination of the above algorithm shows that the difficulty of model reduction for singular systems is to retain its impulsive nature. Thus, based on this observation, we investigate the impulsive controllability and impulsive observability of singular systems and propose a new decomposition approach for singular systems. Then a new model reduction algorithm is designed based on the new decomposition via the machinery of Nehari´s approximation algorithm. This new model reduction algorithm retains the impulsive nature of the original system. Finally, an example is presented to illustrate the effectiveness of the proposed model reduction algorithm