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This brief deals with the adaptation of a real-time controller's sampling period to account for the available computing resource variations. The design of such controllers requires a parameter-dependent discrete-time model of the plant, where the parameter is the sampling period. A polytopic approach for linear parameter varying (LPV) systems is then developed to get an H∞ sampling period dependent controller. A reduction of the polytope size is here performed which drastically reduces the conservatism of the approach and makes easier the controller implementation. Some experimental results on a T-inverted pendulum are provided to show the efficiency of the approach.