| Model reduction/approximation problems arise in many scientific and engineering disciplines. In the study of dynamics and control of LTI systems, low order models are normally preferred over high order ones, whether from open loop computation or feedback design viewpoints. For this reason, there is a desire to have methods available to obtain reduced order approximation for high order systems. This dissertation proposes a model reduction algorithm from the factorization approach, which is referred to as the Normalized Coprime Factor Model Reduction Algorithm (NCFMR). This algorithm is an application of state-space truncation to a specially balanced coordinate system. It suggests to obtain a low order model by reducing the intricacy of the coprime factors (or, graph operators) of a complicated model. At the center of the algorithmic development is the balancing of a pair of algebraic Riccati equations (AREs), whose solutions are used to construct the state space matrices of the system's normalized coprime factors. The balancing of the AREs is observed to be equivalent to the balancing of some Lyapunov equations in the generalized sense. By making use of this property, an upper bound on the graph metrics is developed for the evaluation of model reduction error and the analysis of robustness. In addition, this dissertation presents numerical examples to support the theoretical arguments, as well as draws a couple of suggestions for future research work. |
