This paper proposes a stability analysis procedure of fluid power components according to some early design parameters. It is based on the numerical determination of the existence of a Lyapunov function, which guarantees the required performance. This is formulated as an optimization problem under Linear Matrix Inequalities constraints (LMIs). The model-based procedure is illustrated with an application to a pneumatic two-stage pressure regulation valve. The results show the method capability to provide a better understanding of the possible causes of the valve’s instability and how it can be avoided at an early design stage by tuning the physical parameters in order to guarantee a desired dynamical behavior and improve system robustness.