This paper concerns the stability analysis of non-linear, switching control laws for pneumatic actuators. A first approach to the problem has been proposed by the authors in [1], under the hypothesis of a simplified model of friction. The approach is based on casting the closed-loop system into a piecewise-affine form. However, if a more realistic friction model is introduced, the method in [1] proves to be too conservative, and unfit to deal with the sliding modes that can occur with this new model. This paper proposes a new method for proving the stability on the system by introducing a less conservative class of Lyapunov function, namely piecewise-polynomial ones. At the end of the paper, we show how such a method can be successfully applied to our experimental setup.