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 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 sys- tem 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.