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Specific low-bitrate coding strategies are examined through their effect onLQ control performance. By limiting the subject to these methods, we are ableto identify principles underlying coding for control; a subject of significantrecent interest but few tangible results. In particular, we consider coding thequantized output signal deploying period-two codes of differingdelay-versus-accuracy tradeoff. The quantification of coding performance is viathe LQ control cost. The feedback control system comprises the coder-decoder inthe path between the output and the state estimator, which is followed bylinear state-variable feedback, as is optimal in the memoryless case. Thequantizer is treated as the functional composition of an infinitely-long linearstaircase function and a saturation. This permits the analysis to subdivideinto estimator computations, seemingly independent of the control performancecriterion, and an escape time evaluation, which ties the control back into thechoice of quantizer saturation bound. An example is studied which illustratesthe role of the control objective in determining the efficacy of coding usingthese schemes. The results mesh well with those observed in signal coding.However, the introduction of a realization-based escape time is a noveltydeparting significantly from mean square computations.

LQG Control Performance with Low Bitrate Periodic Coding