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Data-based control design methods most often consist of iterative adjustment of the controller&psila;s parameters towards the parameter values which minimize an H2 performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization - no process model is used. A limiting factor in the application of these methods is the lack of useful conditions guaranteeing convergence to the global minimum; several adaptive control algorithms suffer from the same limitation. In this paper the H2 performance criterion is analyzed in order to characterize and enlarge the set of initial parameter values from which a gradient descent algorithm can converge to its global minimum.