## A study on decentralized $$H_{\infty}$$ feedback control systems with local quantizers.(English)Zbl 1158.93350

Summary: 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.

### MSC:

 93C15 Control/observation systems governed by ordinary differential equations 93C55 Discrete-time control/observation systems 93C83 Control/observation systems involving computers (process control, etc.) 93D15 Stabilization of systems by feedback 93D25 Input-output approaches in control theory
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### References:

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