H∞ control of LFT systems: an LMI approach

The standard H∞ control problem for linear state-space systems is extended to general LFT systems, which involve a LFT (linear fractional transformation) on a structured free parameter Delta and can be interpreted as structuredly perturbed uncertain systems. Two generalizations of H∞ performance are considered, referred too as µ-performance and Q-performance with the latter implying the former. Necessary and sufficient conditions for a system to have Q-performance and for the existence of a controller yielding Q-performance can be expressed in terms of structured linear matrix inequalities (LMIs).