This thesis revisits the singular value based model order reduction technique that was developed in [33] to prove that the solution of the full order model converges to the solution of the reduced order model and to characterize the error between the full order model and the reduced order model.

To prove convergence, a general, stable, linear, time-invariant system is transformed using the technique of [33]. Then, a reduced order model is obtained using the method of matched asymptotics. This reduced order model is the same as that which results

from applying the method of [33] to the original system. The transfer function error is used to perform a low frequency analysis and test for convergence. Three numerical examples are simulated to evaluate the performance of the method in comparison with other well-known methods. In addition, the number of computations that these methods require to produce the reduced order model is noted and compared.

The developments presented in this thesis clearly show that the model order reduction method of [33] is such that the solution of the full order model converges to the solution of the reduced order model, and that the low frequency error is small, while requiring fewer computations than other well-known methods.

[33] A. A. Mohammad, “Modeling issues and the lyapunov equations in dynamical control systems,” Ph.D. diss., University of Akron, 1992.