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This paper addresses the end-to-end sample complexity bound for learning inclosed loop the state estimator-based robust H2 controller for an unknown(possibly unstable) Linear Time Invariant (LTI) system, when given a fixedstate-feedback gain. We build on the results from Ding et al. (1994) to bridgethe gap between the parameterization of all state-estimators and the celebratedYoula parameterization. Refitting the expression of the relevant closed loopallows for the optimal linear observer problem given a fixed state feedbackgain to be recast as a convex problem in the Youla parameter. The robustsynthesis procedure is performed by considering bounded additive modeluncertainty on the coprime factors of the plant, such that a min-maxoptimization problem is formulated for the robust H2 controller via an observerapproach. The closed-loop identification scheme follows Zhang et al. (2021),where the nominal model of the true plant is identified by constructing aHankel-like matrix from a single time-series of noisy, finite lengthinput-output data by using the ordinary least squares algorithm from Sarkar etal. (2020). Finally, a H-infinity bound on the estimated model error isprovided, as the robust synthesis procedure requires bounded additiveuncertainty on the coprime factors of the model.

Sample Complexity for Evaluating the Robust Linear Observers Performance under Coprime Factors Uncertainty