2020/02/14 by Noroozi, Navid, Mironchenko, Andrii, Kawan, Christoph +1
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2002.07085
Motivated by a paradigm shift towards a hyper-connected world, we develop a computationally tractable small-gain theorem for a network of infinitely many systems, termed as infinite networks. The proposed small-gain theorem addresses exponential input-to-state stability with respect to closed sets, which enables us to analyze diverse stability problems in a unified manner. The small-gain condition, expressed in terms of the spectral radius of a gain operator collecting all the information about the internal Lyapunov gains, can be numerically computed for a large class of systems in an efficient way. To demonstrate broad applicability of our small-gain theorem, we apply it to the stability analysis of infinite time-varying networks, to consensus in infinite-agent systems, as well as to the design of distributed observers for infinite networks.