This paper discusses a design method for a single-input single-output multi-rate sampled-data control system, where the sampling interval of a plant output is an integer multiple of the hold interval of a control input. In such a sampled-data control system, the intersample output can oscillate even if the sampled output converges to the reference input. Because of the oscillation, heavy load is on the actuator, and the control performance is deteriorated. To resolve the problem, in a conventional method, a control law is extended using the null-space, and the intersample response is improved such that the sampled response is maintained. The conventional method has been designed based on the transfer function representation. In the proposed method, on the state-space representation, the null-space is introduced, and the existing control system is extended. Finally, through numerical examples, the effectiveness of the proposed method is verified.
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