This article deals with the robust control design problem for linear time invariant systems affected by variable feedback delay. Constraints on the system state are considered in the system description. The starting point is the construction of a predictive control law which guarantees the existence of a nonempty robust positive invariant (RPI) set with respect to the closed-loop dynamics. Subsequently, an iterative algorithm is proposed in order to obtain an approximation of the maximal RPI set. The problem can be treated in the framework of piecewise affine systems due to the explicit formulations of the control law obtained via multiparametric programming.