Data-based control design methods most often consist of iterative adjustment of the controller's parameters towards the parameter Values which minimize an H-2 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 H-2 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. (C) 2008 Published by Elsevier Ltd