Combining a 4 x 4 transfer matrix formalism and nonlinear slowly varying envelope approximation we obtain a simple method to describe analytically steady states associated with dispersive multistability in N coupled microring resonators. We applied this formalism to the reduction of the multistability threshold in coupled microrings. This approach allows us to consider nonlinear interactions between independent forward and backward propagative fields in an instantaneous dispersive local Kerr material microring. Finally, we applied it to control optically the tristable regime of a microring.