Stable phantom-divide crossing in two-scalar models with matter

We construct cosmological models with two scalar fields, which have a structure as in the ghost condensation model or k-essence model. The models can describe a stable phantom crossing, which should be contrasted with one-scalar tensor models, where the infinite instability occurs at the crossing the phantom divide. We give a general formulation of the reconstruction in terms of the e-foldings N by including the matter although in the previous two-scalar models, which are extensions of the scalar tensor model, it was difficult to give a formulation of the reconstruction when we include matter. In the formulation of the reconstruction, we start with a model with some arbitrary functions, and find the functions which generate the history of the expansion of the universe. We also give general arguments for the stabilities of the models and the reconstructed solution. The viability of a model is also investigated by comparing to the observational data.