Optimal Relation Between Quantization Precision and Sampling Rates

In this chapter, the problem of the control over limited bandwidth communication channels is addressed. A finely grained model is adopted. Such a model ensures the respect of the bandwidth constraints and allows the influence characterization of update frequency and quantization precision on the control performance. A simple static strategy is first proposed, and its (W,V)-stability properties are studied. An efficient approach for the improvement of disturbance rejection capabilities and steady state precision are then proposed. This approach dynamically assigns the quantization precision of the control signals in order to improve the control performance by taking into account the communication and computation requirements of the introduced dynamic protocol. It naturally allows handling linear time invariant systems (LTI) with multiple inputs. Sufficient conditions for ensuring the practical stability of this approach are stated. Finally, the proposed approach is evaluated and illustrated through a numerical example.

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