This work focuses on the congestion control design for ad hoc networks affected by time-delay and asymmetrical input saturation. First, an innovative general TCP/AQM model for mobile and wireless ad hoc networks (MANET/WANET) is proposed using graph theory and TCP/AQM system dynamics in a dumbbell topology. Next, a new characteristic condition for sector linearity is developed, which plays the role of a specification to be checked and allows us to assume that the dynamics of the nodes are not saturated. Finally, we propose a new consensus-based congestion control protocol while satisfying the input constraints based on the Lyapunov method, the new sector of linearity condition, the Bessel Legendre-based integral inequality, and the reciprocal convex combination. The proposed results have the advantage of being given as a set of linear matrix inequality (LMI) conditions, which can be solved using convex optimization toolboxes. The merits of the theory are evaluated with the help of various real and challenging scenarios with the use of MATLAB and NS3.