This paper addresses the problem of optimal and robust H-2 control for discrete-time periodic systems with Markov jump parameters and multiplicative noise. To analyse the system performance in the presence of exogenous random disturbance, an H-2 norm is firstly established on the basis of Gramian matrices. Further, under the condition of exact observability, a necessary and sufficient condition is presented for the solvability of H-2 optimal control problem by means of a generalised Riccati equation. When the transition probabilities of jump parameter are incompletely measurable, an H-2-guaranteed cost norm is exploited and the robust H-2 controller is designed through a linear matrix inequality (LMI) optimisation approach. An example of a networked control system is supplied to illustrate the proposed results.