This paper proposes a numerical approach to the stability analysis for a class of piecewise-affine systems with (possibly time-varying) parameter-dependent cells and dynamics. This class of model aims at allowing a better modelling of time-varying or parameter-varying nonlinearities of physical phenomena such as dry friction. We form the stability certification problem as the one of finding a Lyapunov function that is parameterised as a polynomial function of the variable parameter. The application of the well-known Lyapunov stability theorem together with the use of the generalised S-procedure reduces the problem to checking whether a certain set of matrices has the sum-of-squares property. The latter can be solved using well-documented numerical solvers, and we provide two examples of successful applications at the end of the paper.