Some Extensions of the Open-Loop Balanced Approach for Model Reduction

This paper provides some extensions of a powerful open-loop model reduction technique called balanced realization. Developed by Moore, this approach uses concepts of controllability and observability to determine a reduced-order model. Moore´s work was developed for controllable, observable, and asymototically stable systems. This paper shows that balancing techniques can be easily extended to unstable systems. Furthermore, using another model reduction method, called chained aggregation, the balanced and chained aggregation methods can be easily combined for systems that are also unobservable and uncontrollable.