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Distributed Stabilization by Probability Control for Deterministic-Stochastic Large Scale Systems : Dissipativity Approach

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Σ$ and a stochastic memoryless map $Ψ$. After that, we extend the result to the class of large scale systems in which: $Σ$ consists of many sub-systems; and $Ψ$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.