Energy efficiency is a measure of performance in wireless networks. Therefore, controlling the transmitter power at a given node increases not only the operating life of the battery but also the overall system capacity by successfully admitting new links between a source and a destination. It is essential to find effective means of power control of point-to-point, broadcasting and multicasting scenarios. The wireless networking presents formidable challenges and we consider the problem of

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... t or point to point (peer-to-peer) communication in wireless networks in the presence of other nodes. We study the feasibility of admitting new links in an operating area in a wireless network while maintaining the quality of service (QoS) in terms of Signal to Interference ratio (SIR) for each link. The SIR is maintained by adjusting the transmitter power levels at each source for a given link. Distributed power control (DPC) is a natural choice for such purposes because, unlike centralized power control, DPC should be able to adjust the power levels of each transmitted signal using local measurements, so that in a reasonable time, all nodes/links will maintain the desired SIR. In this paper, we present a suite of DPC schemes using both the state space and optimal control methodology in discrete-time. Further, we prove the convergence of the overall network with our algorithm using Lyapunov stability analysis in comparison with an available DPC scheme in the literature. We present simulation results and comparisons to one of the well known DPC scheme in the literature for point to point communications in the case of overlapping scenario.