Data networks
Introduction to algorithms
Deterministic and Stochastic Time-Delay Systems
Deterministic and Stochastic Time-Delay Systems
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We outline a methodology to determine the reachability bound of a homogeneous interactive power network (IPN) with wireless distributed control by using a piecewise linear (PWL) model of the system. By formulating a convex optimization problem based on a composite Lyapunov function and solving this problem using linear-matrix-inequality solvers, we predict the reaching criteria for orbital existence. We investigate the impacts of time delays due to the wireless network and communication-channel disruptions on the reachability bound and performance of the IPN. Because of the infeasibility of modeling such network control systems (NCS) in a deterministic framework, we adopt a probabilistic approach based on Markov chains to model the wireless network and incorporate them into the PWL models of the system. Using these models, we analyze the reaching conditions of the IPN in a probabilistic domain and comment on the mean-square stability of the system. Further, we demonstrate how communication fault-tolerant protocols can be implemented to ensure that the IPNs operate within their reachability and performance bounds, despite one or more disruptions in the communication channels.