Worst-case error analysis of the balanced-matrix method of model reduction

Worst-case error analysis, which was previously obtained for the aggregation method of model reduction, is given for the balanced-matrix method. A worst-case error is constructed for balanced reduced-order models approximating a given linear time-invariant, completely controllable, completely observable balanced system. Also, it is shown that the worst-case error bounds can apply to reduced-order models obtained using other reduction methods. When the model and the full-scale system are balanced, the computations to obtain the error bounds are simplified. Several numerical examples are given.