This research delves into optimizing dynamic systems by employing Kautz parametrization in Model Predictive Control (MPC) for constrained linear-time varying systems. Dynamic systems often require adaptive control strategies to accommodate changing conditions and constraints. Kautz parametrization offers a versatile framework for the representation of linear-time varying systems. This study explores the integration of Kautz parametrization into MPC, a powerful control technique for constrained systems. Through theoretical analysis and simulations, the research aims to demonstrate the advantages of this approach in enhancing the performance and adaptability of control systems in dynamic environments.