Efficient Criteria for Stability of Large-Scale Networked Control Systems*

In this paper, we analyze the stochastic stability of a class of large-scale networked control systems. We specifically consider spatially connected linear time-invariant systems whose communication with adjacent subsystems is subject to data losses. We first show that a direct application of the stability theory of Markov jump linear systems provides stability conditions in terms of the eigenvalues of a matrix whose size grows exponentially with the number of subsystems. To overcome this limitation, using the spectrum theory of random matrices, we then derive an alternative stability condition in terms of a matrix whose size grows linearly with the number of subsystems in the network. We illustrate our results with numerical simulations.