This paper concerns the control of pneumatic actuators, which are nowadays of widespread use in the industry. A problem related to the use of such actuators is the so-called “stick-slip”, due to the presence of dry friction on the system. A switching control law has been proposed in the literature in order to avoid this phenomenon, without giving a formal proof of the closed-loop stability of the system; the absence of a proof was due to the difficulty of finding a Lyapunov function, and to the fact that the state converges not to a single point but to a set. In this article, we prove stability by modelling the pneumatic system and its switching control law as a piecewise affine system. This formalism allows the use of a variety of specific techniques, which we have extended in order to cast the proof of the convergence of the state as a Linear Matrix Inequality (LMI) test. The paper contains the description of our experimental setup and the results obtained by applying the aforementioned method.