In this paper, we make a foray in the role played by a set of four operators on the study of robust H-2 and mixed H-2/H control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H-2 performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H-2 controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H-2/H controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm.