Convergence of distributed WSN algorithms: The wake-up scattering problem

In this paper, we analyze the problem of finding a periodic schedule for the wake-up times of a set of nodes in a Wireless Sensor Network that optimizes the coverage of the region the nodes are deployed on. An exact solution of the problem entails the solution of an Integer Linear Program and is hardly viable on low power nodes. Giusti et. al. [6] have recently proposed an efficient decentralized approach that produces a generally good suboptimal solution. In this paper, we study the convergence of this algorithm by casting the problem into one of asymptotic stability for a particular class of linear switching systems. For general topologies of the WSN, we offer local stability results. In some specific special cases, we are also able to prove global stability properties.