Toward a stability monitoring system of an asset-communications network exposed to malicious attacks

This paper proposes stability conditions for a network of assets. The assets are connected to a communications network, thus constituting a two-layered (or two-tier) network. The effectiveness of the network, and even its stability, can be indirectly affected by malicious attacks targeting the communications. The particular case of virus propagation on the assets is considered. The network of assets is modeled as a discrete-time, jump, linear system whose transitions are governed by nonlinear discrete-time dynamics representing a class of virus diffusion. The state-space variables of the latter represent the probabilities of each node receiving the virus and being infected. The stability analysis is obtained by means of a stochastic Lyapunov function argument and yields a sufficient condition expressed as a linear matrix inequality (LMI). This LMI involves the asset state-space matrices and the positive limit set of the probabilistic model of the virus propagation dynamics, which exhibits the attraction property provided a sufficient condition is satisfied. The proposed condition involves the adjacency matrix of the communications network and the parameters characterizing virus propagation. An approximation to the sufficient condition is proposed so that convergence of the system trajectories could be monitored online. The analysis is extended to a class of jump systems, which are affinely excited by some disturbance, yielding an almost-sure boundedness of the trajectories.