The H-2 performance specification for one-dimensional (1-D) systems has been known to be analytically and practically meaningful and widely applied to the analysis and design of control and signal processing systems. However, there has been few results on the analysis and design of two-dimensional (2-D) systems using the H-2 performance specification due to the structural and dynamical complexity of 2-D systems. In this paper, we extend the classical definition of the H-2 performance to 2-D systems and present a sufficient condition for evaluation of the H-2 performance of 2-D systems in Roesser model. Using this condition and the existing bounded real lemma, we develop systematic design methods for H-2 and mixed H-2/Hcc control of 2-D systems, and an application of the controller design methods to the control problem of a metal rolling process is demonstrated in this paper. (C) 2006 Elsevier Ltd. All rights reserved.