This work proposes a single-step, LMI based synthesis method for the design of robust, distributed and fixed-order output-feedback controllers based on the sparsity invariance framework and the full block S-Procedure. The theoretic results are applied to the optical synchronization system at the European XFEL, which can be modeled as a distributed system of input-output connected, phase-locked oscillators. Whereas in recent work a decentralized controller structure for the nominal system was synthesized, this work continues to develop the synthesis method and adds robustness guarantees to the generated solution. We show simulation results motivated by the real application and demonstrate that, compared to the nominal decentralized solution, no additional conservatism is introduced by the robust solution, if the uncertainty approaches the nominal value.
