Stabilizing scheduling logic for networked control systems under limited capacity and lossy communication networks

In this paper we address the problem of designing scheduling logic for stabilizing Networked Control Systems (NCSs) with plants and controllers remotely-located over a limited capacity communication network subject to data losses. Our specific contributions include characterization of stability under worst case data loss using an inequality associated with a cycle on a graph. This is eventually formulated as a feasibility problem to solve for certain parameters ($T$-factors) used to design a periodic scheduling logic. We show that given a solution to the feasibility problem, the designed scheduling logic guarantees \emph{global asymptotic stability} for all plants of the network under all admissible data losses. We also derive sufficient conditions on the number of plants and the capacity of the network for the existence of a solution to the feasibility problem. Given that a sufficient condition is satisfied, we discuss the procedure to obtain the feasible $T$-factors. We use tools from switched systems theory and graph theory in this work. A numerical experiment is provided to verify our results.