Finite Horizon Robust Synthesis

This paper presents 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 described by time-domain Integral Quadratic Constraints (IQCs). The objective is to synthesize a controller to minimize the worst-case performance. This leads to a nonconvex optimization. The proposed approach alternates between an LTV synthesis step and an IQC analysis step. This is analogous to the existing D-K iteration method. Both L₂ and terminal Euclidean norm penalties on output are considered for finite horizon performance. A simple example is provided to demonstrate the proposed algorithm.