  We show how to compose robust stability tests for uncertain systems modeled
as linear fractional representations and affected by various types of dynamic
uncertainties. Our results are formulated in terms of linear matrix
inequalities and rest on the recently established notion of finite-horizon
integral quadratic constraints with a terminal cost. The construction of such
constraints is motivated by an unconventional application of the S-procedure in
the frequency domain with dynamic Lagrange multipliers. Our technical
contribution reveals how this construction can be performed by dissipativity
arguments in the time-domain and in a lossless fashion. This opens the way for
generalizations to time-varying or hybrid systems.
