Feedback type dynamic quantizers such as delta-sigma modulators are typically effective for encoding high-resolution data into lower resolution data. The dynamic quantizers include a filter and a static quantizer. When it is required to control under a communication rate constraint, the data rate of the quantizer output should be minimized appropriately by quantization. This technical note provides numerical methods for the complete design of a type of dynamic quantizers, including the selection of all the quantizer parameters in order tominimize a specific performance index and satisfy a communication constraint. The design method of the dynamic quantizer is proposed using a particle swarm optimization (PSO) method. A part of the initial quantizers in PSO are designed based on an invariant set analysis and an iteration algorithm. Effectiveness of the system with the proposed quantizer is assessed through numerical examples.