This thesis investigates the frequency weighted balanced model reduction problem for linear time invariant systems. First, an interesting property of well-known frequency weighted balanced model reduction techniques (Enns', Lin and Chiu's, Wang et al's, Varga and Anderson's), is derived with special types of weighting functions. The special functions considered here are co-inner and inner functions, for input and output weights respectively. The derivations are carried out for both continuous-time and discrete-time systems. The results are then illustrated using numerical examples. Two new frequency weighted balanced model reduction techniques, based on partial fraction expansion idea, are then developed. These methods yield stable models even when two sided weightings are applied. A priori error bounds for the model reduction methods are derived. Lower weighted errors and error bounds are obtained using free parameters. The results are then illustrated using several numerical examples, including those involving practical applications to show the e ectiveness of the methods. We then proceed with an alternative frequency weighted balanced model reduction method which is based on Schur decomposition. This method yields a sigini cant improvement on Lin and Chiu's technique. Two a priori error bounds for the model reduction method are derived. Lower approximation errors and error bounds are obtained using free parameters. Finally, the results are illustrated using several numerical examples including those involving robot controller reduction applications.
|Qualification||Doctor of Philosophy|
|Publication status||Unpublished - 2009|