Model reduction using balance-truncation method with lower error bounds

A modified balance-truncation reduced-order model is developed by introducing a weighting factor which provides an extra degree of freedom in emphasizing the relative magnitude of the model reduction errors at low and high frequencies. The maximum model reduction error can be reduced to a lower value by an appropriate choice of the weighting factor. The direct model of B.C. Moore (1982) and the singular perturbation approximation method will become two special cases in the modified technique. A stability criterion for the reduced-order model and a procedure for selection of the weighting factor are developed. The formulae for the L_∞-norm error bound on the reduction at zero and infinite frequencies are also derived. The proposed model reduction method is demonstrated by designing lower-order controllers for a Phillips Laboratory experimental flexible grid structure