# Abstract:

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.

# Keywords:

output feedback, decentralized $H_{\infty}$ feedback control system, quantizer, quantization, matrix inequality

# Classification:

93C15, 93C55, 93C83, 93D15, 93D25