Performance Robustness for LTI Systems with Structured State Space Uncertainty

Performance robustness of an LTI system with structured state space uncertainty is considered by using the Gronwall lemma approach. A recent sufficient condition for stability robustness is extended to ensure that the closed loop eigenvalues lie within chosen performance regions when the LTI system is subjected to time-invariant structured state space uncertainty. The conservatism of the performance robustness condition is addressed by introducing a unitary weighting matrix in addition to the earlier real positive diagonal weighting. An example of the lateral dynamics of the L-1011 aircraft is presented to illustrate the new performance robustness result and the usefulness of the unitary weighting matrix in satisfying the sufficient condition.