The paper addresses the problem of determination of guaranteeing cost control strategies for discrete-time two-persons zero-sum non-linear games over infinite horizon. In the proposed approach the objective functional is appropriately modified in order to cope with the uncertainties, and a sufficient condition is given to ensure that a given state-feedback is a guaranteeing cost control. The results are applied also for linear systems with uncertainties of linear fractional structure to derive guaranteeing cost strategies for both players. It is shown that this approach can successfully be applied in this case, when the method of introducing fictitious games as proposed in previous papers may come up against a difficulty. The results are illustrated by numerical examples.