Abstract—In recent years, there have been many studies with different order reduction algorithms to solve model order reduction problems. However, most of the proposed algorithms are mainly applicable to stable linear systems. In practical applications, many problems require order reduction of an unstable continuous system. Therefore, order reduction algorithms need to be able to reduce the order of an unstable continuous system. This paper introduces two balanced truncation algorithms based on mapping applied to unstable continuous systems. By flexibly using the continuous-continuous mapping to transform an unstable continuous system to a stable continuous one and vice versa, the first balanced truncation algorithm can reduce the order of the unstable continuous system. The second balanced truncation algorithm flexibly applies continuous-discrete mapping to convert an unstable continuous system to a stable discrete system and vice versa to help the algorithm reduce the order of the unstable continuous system. Applying two algorithms to reduce the order of the 15th-order unstable system shows that the 5th and 4th-order reduced systems can replace the 15th-order unstable system. The results have demonstrated the correctness of the algorithms and opened the possibility of applying algorithms in practice.
 
Keywords—model order reduction, balanced truncation algorithm, continuous-continuous mapping, continuous-discontinuous mapping


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