Robustness with dynamic IQCs: An exact state-space characterization of nominal stability with applications to robust estimation

For robustness analysis with integral quadratic constraints, we formulate a new positivity condition on the solution of the corresponding linear matrix inequality which is necessary and sufficient for nominal stability of the underlying system. The application of this technical result is illustrated by a complete solution of the L2L2-gain and robust H2H2-estimator design problems if the uncertainties are characterized by dynamic integral quadratic constraints.