This article deals with the model predictive control (MPC) design problem for systems which are linearly dependent on a time-varying parameter. The main novelty is that, motivated by practical issues, the bounds on the rate of variation of the parameters are taken into account in the control design. Moreover, a Lyapunov function depending multiaffinely on the parameters computed at a set of instants of time and a parameter-dependent control gain are used to provide an upper bound to a quadratic performance index. The solution is obtained by means of a semidefinite programming algorithm. Examples illustrate the efficiency of the proposed approach.