A switched system model for stability analysis of distributed power control algorithms for cellular communications

We examine the well known distributed power control (DPC) algorithm proposed by Foschini and Miljanic and show via simulations that it may fail to converge in the presence of time-varying channels and handoff, even when the feasibility of the power control problem is maintained at all times. Simulation results also demonstrate that the percentage of instability is a function of the variance of shadow fading, interference and the target signal to interference plus noise ratio. In order to better explain these observations and provide a systematic framework to study the stability of distributed power control algorithms in general, we present the problem in the context of switched systems, which can capture the time variations of the channel and handoffs. This formulation leads to interesting stability problems, which we address using common quadratic Lyapunov functions and M-matrices.