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In this paper, the authors consider stability analysis on WMN-based network control system with the optimum transmission condition. By establishing the optimum transmission model of the wireless mesh network, they get the minimum transmission delay. Then they propose a new Lyapunov stability criteria, which adapts to the stability of WMN-based network control system under the circumstance of the optimum transmission condition. According to the analysis and calculation, the results show that the optimum transmission condition and the corresponding stability may vary by different congestion conditions and levels of path demand.
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