A new quantization-dependent Lyapunov function is proposed to analyze the\r\nquantized feedback stabilization problem of systems with multiplicative noise. For\r\nconvenience of the proof, only a single-input case is considered (which can be\r\ngeneralized to a multi-input channel). Conditions for the systems to be quantized\r\nmean-square poly-quadratically stabilized are derived, and the analysis of H8\r\nperformance and controller design is conducted for a given logarithmic quantizer.\r\nThe most significant feature is the utilization of a quantization-dependent Lyapunov\r\nfunction, leading to less conservative results, which is shown both theoretically and\r\nthrough numerical examples.
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