Multi-agent linear systems with noise. Solving decoupling problem

Dynamical multi-agent systems are being extensively studied by researchers in the field of control theory. It is due to the multi-agents appear in different study subjects as for example in the consensus problem of communication networks, formation control of mobile robots or cooperative control of unmanned aerial vehicles. The disturbance decoupling problem for linear dynamical systems with noise was the starting point for the development of a geometric approach to systems theory. The problem consists in that the disturbance not interfere with the solution of the linear dynamical system; in other words, to find a compensator such that the closed loop transfer matrix from disturbance to output is 0. Several multiagents linear systems are affected by noises, nevertheless almost all the existing results in consensus problem, do not take into account the effects of these noises. The goal of this paper is to advance in the study of the consensus problems under noise disturbances using linear algebra techniques. Key–Words: Multi-agent systems, consensus, controllability, observability, output-controllability, disturbance decoupling problem.