Rank constrained stabilization of complex networks

Abstract

In this paper global stabilization of a complex network is attained by applying local decentralized output feedback control to a minimum number of nodes of the network. The stabilization of the network is treated as a rank constrained problem. Necessary conditions for stabilization of a complex network is derived as a convex LMI representation. Strict positive realness conditions on the node level dynamics allow nonlinearities/uncertainties which satisfy sector conditions to be considered. A randomly generated academic example with 20 nodes is used to demonstrate the efficacy of the approach.