Geodesic
A study on decentralized $H_\infty$ feedback control systems with local quantizers
Kybernetika, Tome 45 (2009) no. 1, pp. 137-150.

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In this paper, we study decentralized $H_{\infty}$ feedback control systems with quantized signals in local input-output (control) channels. We first assume that a decentralized output feedback controller has been designed for a multi-channel continuous-time system so that the closed-loop system is Hurwitz stable and a desired $H_{\infty}$ disturbance attenuation level is achieved. However, since the local measurement outputs are quantized by a general quantizer before they are passed to the controller, the system's performance is not guaranteed. For this reason, we propose a local-output-dependent strategy for updating the quantizers' parameters, so that the closed-loop system is asymptotically stable and achieves the same $H_{\infty}$ disturbance attenuation level. We also extend the discussion and the result to the case of multi-channel discrete-time $H_{\infty}$ feedback control systems.
Classification : 93A14, 93B36, 93C15, 93C55, 93C83, 93D15, 93D25
Keywords: decentralized $H_{\infty}$ feedback control system; quantizer; quantization; matrix inequality; output feedback 
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     author = {Zhai, Guisheng and Chen, Ning and Gui, Weihua},
     title = {A study on decentralized $H_\infty$ feedback control systems with local quantizers},
     journal = {Kybernetika},
     pages = {137--150},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {2009},
     mrnumber = {2489585},
     zbl = {1158.93350},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009__45_1_a9/}
}
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Zhai, Guisheng; Chen, Ning; Gui, Weihua. A study on decentralized $H_\infty$ feedback control systems with local quantizers. Kybernetika, Tome 45 (2009) no. 1, pp. 137-150. http://geodesic.mathdoc.fr/item/KYB_2009__45_1_a9/