  We present a robust synthesis algorithm for uncertain linear time-varying
(LTV) systems on finite horizons. The uncertain system is described as an
interconnection of a known LTV system and a perturbation. The input-output
behavior of the perturbation is specified by time-domain Integral Quadratic
Constraints (IQCs). The objective is to synthesize a controller to minimize the
worst-case performance. This leads to a non-convex optimization. The proposed
approach alternates between an LTV synthesis step and an IQC analysis step.
Both induced $\mathcal{L}_2$ and terminal Euclidean norm penalties on output
are considered for finite horizon performance. The proposed algorithm ensures
that the robust performance is non-increasing at each iteration step. The
effectiveness of this method is demonstrated using numerical examples.
