On the stability of a power control algorithm for wireless networks in the presence of time-varying delays

This paper studies the robustness of the well known Foschini-Miljanic power control algorithm with respect to time-varying delays. Since delays are omnipresent in wireless networks, this problem is of practical importance. It has been proven in the past that no matter how large the delays are, the Foschini-Miljanic algorithm still converges. However, this was based on the assumption that the delays are constant over time, which is not always met in practice. Therefore, the problem addressed in this paper is how the algorithm behaves under the time-varying delays case. Firstly, we provide the conditions under which the system is stable by means of a Linear Matrix Inequality (LMI) and using a semi-definite optimization solver we show the validity of our results through illustrative examples.