This paper analyzes performance of periodically time-varying sampled data controllers for L-P deterministic and uniform disturbance rejection, For a given linear periodic sampled data controller controlling a linear time-invariant continuous-time plant, it is shown that a linear time-invariant controller can be found to give better L-P sampled data control than the time-varying controller. The performance analysis is in time domain using convexity properties of the L-P signal space.