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**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 |

### Keywords:

decentralized \(H_{\infty}\) feedback control system; quantizer; quantization; matrix inequality; output feedback### References:

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