Stability of a general class of distributed algorithms for power control in time-dependent wireless networks

We consider a general class of distributed algorithms for the control of power allocations in time-dependent wireless networks. We employ appropriately constructed Lyapunov functions to show that any bounded power distribution obtained from these algorithms is uniformly asymptotically stable. Further, we use Lyapunov-Razumikhin functions to show that even when the system incorporates heterogeneous, time-varying delays, any solution along which the generalized system nonlinearity is bounded must also be uniformly asymptotically stable. Moreover, in both of these cases this stability is shown to be global, meaning that every power distribution must have the same asymptotic behavior.