Towards the Control of Linear Systems with Minimum Bit-Rate

We address the problem of determining the minimum bit-rate needed to stabilize a linear time-invariant process. For the noise free case, we determine a bit-rate below which stabilization is not possible and above which asymptotic stabilization can be achieved. Inspired by differential pulse code modulation (DPCM) techniques, we propose practical encoding/decoding schemes that guarantee boundedness of the state for the case of a noisy linear time-invariant process. With fixed-step quantization, we are only able to approach the minimum bit-rate for the noiseless case. However, with variable-step quantization we are able to approach it even in the presence of noise and disturbances.