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In this paper, we present a new cautious H₂ optimal design approach based on the noisy and biased Markov parameters identified from a finite number of input and output samples in a closed-loop plant. This approach not only links closed-loop subspace identification with optimal control; but also directly evaluates parametric uncertainties on the identified Markov parameters. Neither a state-space model nor its stochastic uncertainty has to be realized. The effects of the parametric uncertainties on the output predictor and a quadratic cost function are explicitly analyzed. An H₂ optimal control problem is formulated as a “minmax” problem of the expectation of the cost function with respect to the stochastic noise in the identified parameters. Analytic solution to this problem is derived in a closed form, which avoids computing the empirical mean of the quadratic cost as required by randomized algorithms. An extension of …