iISS and ISS of CDMA Power Control with Respect to Disturbances in The Presence of Delays: A Lyapunov-Krasovskii Approach

摘要

In this paper, we focus on robustness of a gradient-type CDMA power control algorithm for wireless communication networks. In addition to disturbances representing power noises and unmodeled secondary interference from neighboring cells, non-uniform time-delays arising in individual channels between mobiles and a base station are taken into account. To verify desired robustness properties, Lyapunov-Krasovskii functionals are explicitly constructed by means of an iISS small-gain theorem. For arbitrarily large time-delays, this paper shows that the power control system retains integral input-to-state stability with respect to the disturbances for a reasonably large class of pricing functions determining the gradient. A stronger property called the input-to-state stability is proved for unbounded gradients.