Tracking Performance Limitations under Disturbance or Uncertainty

This paper investigates tracking performance limitations of a linear time invariant (LTI) multivariable plant subject to external disturbance or model uncertainty. It attempts to extend some recent results on tracking performance limitation in which neither the disturbance nor the uncertainty is considered. The reference signal to be tracked is a step signal. The tracking performance is measured by the energy of the tracking error. The external disturbance is assumed to be energy bounded and to be injected into the input channels of the plant. The model uncertainty is assumed to have some special structure and to have certain induced norm bound. The performance limitation studied is the minimal attainable value, under any controller structure and parameters, of the maximum tracking error energy for all possible disturbance or uncertainty. It is shown that the tracking performance limit of the plant with the worst case disturbance can be decomposed as the sum of the tracking performance limit without the disturbance and the optimal disturbance attenuation performance without the reference. It is also found that, for an LTI plant with a nonlinear time-invariant uncertainty, the best attainable tracking performance of the system under the worst possible uncertainty is proportional to the tracking performance limit of the plant without uncertainty, magnified by a quantity related to the size of the uncertainty and certain optimal H∞ gain.Copyright c ©2005 IFAC