The transmission scheduling scheme of wireless networks for industrial control systems is a crucial design component since it directly affects the stability of networked control systems. In this paper, we propose a novel transmission scheduling framework to guarantee the stability of heterogeneous multiple control systems over unreliable wireless channels. Based on the explicit control stability conditions, a constrained optimization problem is proposed to maximize the minimum slack of the stability constraint for the heterogeneous control systems. We propose three transmission scheduling schemes, namely centralized stationary random access, distributed random access, and Lyapunov-based scheduling scheme, to solve the constrained optimization problem with a low computation cost. The three proposed transmission scheduling schemes were evaluated on heterogeneous multiple control systems with different link conditions. One interesting finding is that the proposed centralized Lyapunov-based approach provides almost ideal performance in the context of control stability. Furthermore, the distributed random access is still useful for the small number of links since it also reduces the operational overhead without significantly sacrificing the control performance.
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