  This paper considers the problem of solving a symmetric positive definite
system of linear equations over a network of agents with arbitrary asynchronous
interactions and membership dynamics. The latter implies that each agent is
allowed to join and leave the network at any time, for infinitely many times,
and lose all its memory upon leaving. We develop Subset Equalizing (SE), a
distributed asynchronous algorithm for solving such a problem. To design and
analyze SE, we introduce a novel time-varying Lyapunov-like function, defined
on a state space with changing dimension, and a generalized concept of network
connectivity, capable of handling such interactions and membership dynamics.
Based on them, we establish the boundedness, asymptotic convergence, and
exponential convergence of SE, along with a bound on its convergence rate.
Finally, through extensive simulation, we show that SE is effective in a
volatile agent network and that a special case of SE, termed Groupwise
Equalizing, is significantly more bandwidth/energy efficient than two existing
algorithms in multi-hop wireless networks.
