TRUNCATION AND RESIDUALIZATION WITH WEIGHTED BALANCED COORDINATES

Frequency-weighted internally balanced (FWIB) truncation is briefly re viewed. A previous frequency response error analysis for FWIB truncati on is extended, and an exact error bound for the special case of order reduction by one state is presented in terms of the controllability-o bservability measure used in selecting the coordinate to truncate, as well as two additional frequency-dependent variables. An approximate e rror bound for the general case of order reduction by more than one st ate is also developed, under the assumption that only states with smal l controllability-observability measures are truncated. The error boun d is shown to give justification for the FWIB truncation technique bas ed only upon consideration of the controllability-observability measur es. However, the presence of the two additional variables suggests a n ew technique based upon the derived criterion. FWIB residualization is presented, and a frequency response error analysis yields results sim ilar to that found for FWIB truncation. Numerical examples are given t o support the error analysis results, as well as to stress that FWIB t runcation and residualization can be used in a coordinated manner to a chieve higher accuracy than that achievable from either technique used alone.