Abstract
This paper presents an optimal dynamic quantizer synthesis for controlling linear time-invariant systems by the discrete-valued input. The quantizers considered here are in the form of a difference equation, for which we find a quantizer such that the system composed of a given linear plant and the quantizer is an optimal approximation of the given linear plant in the sense of the input-output relation. First, we derive a closed form expression for the performance of the dynamic quantizers in control systems. Next, based on this, an optimal dynamic quantizer and its performance, corresponding to the performance limitation of the dynamic quantizers, are provided. Finally, the relation among the optimal dynamic quantizer and the existing quantizers, the receding horizon quantizers and the ΔΣ modulators, is discussed.
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