Consensus of multicomponent system in changing topology with additive noise

The article focuses on multiagent systems with a fixed number of components. Particles synchronise in discrete moments of time according to a certain set of communication graphs. At every moment of time state of the system is described by a vector that updates iteratively. Each agent's state is determined by states of its neighbours and is influenced by additive noise component. Besides, links between particles change through time. Thus, the evolution of the system can be described as an iterative process where the state vector is multiplied by a certain stochastic matrix and added to a random vector. The aim of this paper is to analyze a value that represents a measure of how close to consensus the system is. The work suggests some restrictions on graphs that are sufficient to obtain an upper bound on that value. Besides, another modified model is presented. It allows relax conditions on graphs and still keep the value bounded.