In this paper buffer dynamic modeling for wireless sensor networks (WSNs) as a highly nonlinear system is accomplished in discrete time and the overall model is gained by blending subsystems obtained based on delay. 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 (LMIs). Moreover, the performance is considered and decay rate is guaranteed. Finally, a set of new LMI-based congestion control schemes (LCC) is obtained for WSNs. The closed-loop systems are globally asymptotically stable (GAS) in case of delay changes resulted from queue size changes. The simulation results using MATLAB and OPNET simulator confirm the effectiveness of our proposed schemes.