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This paper presents the central finite-dimensional H∞ controller for linear systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H∞ controller problem to the corresponding H2 controller problem, using the technique proposed in. The paper yields the central suboptimal H∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H2 controller obtained in. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H∞ controller for linear systems with exactly known parameter values.