An alternative approach for real-time network-wide traffic control in cities that has recently gained a lot of interest is perimeter flow control. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the inter-regional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions, so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of the current work is to study two aspects that are not covered in the perimeter control literature, which are: (a) integration of appropriate external demand information that has been considered system disturbance in the derivation of feedback control laws in previous works, and (b) mathematical formulation of the original nonlinear problem in a linear-parameter-varying (LPV) form, so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem, as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. The developed scheme is applied to microsimulation in order to better investigate its applicability to real life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared to fixed-time control as all the performance indicators are improved significantly.