  This paper presents an approach to compute the worst-case gain of the
interconnection of a finite time horizon linear time-variant system and a
perturbation. The input/output behavior of the uncertainty is described by
integral quadratic constraints (IQCs). A condition for the worst-case gain of
such an interconnection can be formulated using dissipation theory as a
parameterized Riccati differential equation, which depends on the chosen IQC
multiplier. A nonlinear optimization problem is formulated to minimize the
upper bound of the worst-case gain over a set of admissible IQC multipliers.
This problem can be efficiently solved with a custom-tailored logarithm scaled,
adaptive differential evolution algorithm. It provides a fast alternative to
similar approaches based on solving semidefinite programs. The algorithm is
applied to the worst-case aerodynamic load analysis for an expendable launch
vehicle (ELV). The worst-case load of the uncertain ELV is calculated under
wind turbulence during the atmospheric ascend and compared to results from
nonlinear simulation.
