Asymptotically tracking control for discrete time-varying link system to structural balance via determined external stimulations

Abstract

This paper is concerned with the structural balance problem for complex dynamical network with the help of coupling effect related to the external stimulations. Consider a network with time-varying and value-weighted links, which can be regarded as a dynamic system. The link dynamic system is modeled as a Riccati matrix difference equation with the coupling matrix related to the external stimulations. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive a simple criterion for ensuring that the discrete link system asymptotically achieves structural balance, meanwhile, the external stimulations track a corresponding vector signal as well. Simulation examples are given to demonstrate the usefulness of the proposed control scheme in this paper.