Gain Margin of a First Order System with Two Delayed Sensors

Wireless sensor networks allow for the deployment of multiple redundant sensors in a feedback control system. However, inherent delays in the sensor networks have the ability to degrade the performance and stability of the closed loop. This paper addresses the stability robustness of a first order system with two delayed sensors. It is shown that the gain margin of the closed loop system can be modified (increased) based on the appropriate choice of feedback gains (weights) for each delayed sensor. Additionally, the maximum range of gains for which the closed loop system is stable is shown to be a function of the maximum possible cross-over frequency for the closed loop system that in turn is dependent on the magnitude of the larger delay.