The transportation of payloads utilizing multiple drones presents a promising application for lifting heavier loads that exceed the payload capacity of a single drone. However, the cable-suspended payload introduces significant challenges to the system, and this research area remains relatively unexplored. In this work, a novel solution for payload-carrying application is proposed. First, the dynamics of cable-suspended payload transportation using multiple quadrotors, taking into account the influence of drag forces on the quadrotors are studied. A nonlinear optimization is employed to control the payload while distributing the control effort required for manipulating the suspended load over the drones in the formation while ensuring both tension constraints and collision avoidance between drones in the formation. The feasible path commands for formation agents are computed from the optimization. One of the critical aspects for controlling such a system is the load-introduced force, which exhibits rapid and complex variations. To address this, an extended state observer is employed to estimate the load force, eliminating the need for a tension sensor. In pursuit of a robust framework, a formation reset strategy is also developed, allowing to maintain load tracking performance and ensure the safety of formation agents, even in the event of a malfunction in one of the drones. A series of simulations are conducted to validate the effectiveness and robustness against disturbance and suspension failure of the proposed strategy and controllers. Results demonstrate that the whole multi-lift system can handle external disturbances, model uncertainties regarding drone inertia, mass and load mass, as well as suspension failures.