(eng): In this paper, based on queue utilization and channel estimation algorithm, congestion is detected and a suitable rate is selected by an adaptive back-off interval selection. In this paper, a new approach is proposed for controller synthesis of our system based on non-quadratic Lyapunov functions, and a controller is designed to stabilize each subsystem. The controller synthesis results are expressed as a set of Linear Matrix Inequalities . Moreover, the performance is considered and decay rate is guaranteed. Finally, a set of new LMI-based congestion control schemes is obtained for WSNs. The closed-loop systems are globally asymptotically stable in case of delay changes resulted from queue size changes.