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A multi-sector analysis for dynamic quantizer synthesis

This paper considers analysis and synthesis methods of dynamic quantizers for linear feedback systems with discrete-valued signal, which consist of the linear system and the dynamic quantizer. We propose a multi-sector condition such that the quantization error is expressed in terms of the combination of various sector conditions. First, this paper proposes quantizer analysis conditions by using the multi-sector condition and the S-procedure. Second, this paper considers quantizer synthesis conditions based on the multi-sector analysis framework. Our method can design a stable quantizer such that the order of the quantizer is exactly the same as that of the given linear system and the infinite time control performance is always guaranteed. Finally, this paper points out that the proposed methods are helpful compared with the methods based on the invariant set analysis framework through numerical examples.