In this paper, the stability and stabilization problems for marine vessels including surface and underwater vehicles are described. In the marine vessels, there are many and strong nonlinear parameters. These give hard design process and difficulties to us. In this article, at first we make a descriptor system representation as a controlled system to preserve the physical parameters of the system as it is. And we propose a new stability and stabilizability conditions based on the quadratic stabilization approach which gives a solution for the unreasonable problems produced by added mass. That is, the proposed conditions are not interfered with the nonsymmetric matrix constraint. And the stability condition is given by an matrix inequality such that it makes us to obtain a solution easily for something.