Lyapunov-based semistability analysis for discrete-time switched network systems

In this paper, we address semistability analysis of a class of distributed iterative algorithms for discrete-time switched network systems. Semistability is the property whereby every solution that starts in a neighborhood of a Lyapunov stable equilibrium converges to a (possibly different) Lyapunov stable equilibrium. To this end, we use a Lyapunov-based approach to develop a series of sufficient conditions for semistability of discrete-time switched systems. This technique gives us a new perspective to design distributed numerical iterative algorithms for network systems from a dynamical systems viewpoint. Despite the fact that distributed iterative algorithms in general are not dynamical systems, the methods we used for proving convergence of dynamical systems are somehow valid for a large class of distributed iterative algorithms in network systems. The motivation of this paper exactly follows from this general observation. Part of the effort by this paper can be viewed as an attempt to analyze distributed numerical algorithms for network systems from a control perspective.