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We present a framework for systematically combining data of an unknown lineartime-invariant system with prior knowledge on the system matrices or on theuncertainty for robust controller design. Our approach leads to linear matrixinequality (LMI) based feasibility criteria which guarantee stability andperformance robustly for all closed-loop systems consistent with the priorknowledge and the available data. The design procedures rely on a combinationof multipliers inferred via prior knowledge and learnt from measured data,where for the latter a novel and unifying disturbance description is employed.While large parts of the paper focus on linear systems and input-statemeasurements, we also provide extensions to robust output-feedback design basedon noisy input-output data and against nonlinear uncertainties. We illustratethrough numerical examples that our approach provides a flexible framework forsimultaneously leveraging prior knowledge and data, thereby reducingconservatism and improving performance significantly if compared to black-boxapproaches to data-driven control.

Combining Prior Knowledge and Data for Robust Controller Design