Achieving cooperative transportation by aerial robot teams ensures flexibility regarding payloads and robustness against failures, which has garnered significant attention in recent years. This study proposes a flexible decentralized controller for robots and the shapes of payloads in a cooperative transport task using multiple single-rotor robots. The proposed controller is robust to mass and center of mass (COM) fluctuations and robot failures. Moreover, it possesses asymptotic stability against dynamics errors. Additionally, the controller supports heterogeneous single-rotor robots. Thus, robots with different specifications and deterioration may be effectively utilized for cooperative transportation. This performance is particularly effective for robot reuse. To achieve the aforementioned performance, the controller consists of a parallel structure comprising two controllers: a feedback controller, which renders the system strictly positive real, and a nonlinear controller, which renders the object asymptotic to the target. First, we confirm cooperative transportation using 8 and 10 robots for two shapes through numerical simulation. Subsequently, the cooperative transportation of a rectangle payload (with a weight of approximately 3 kg and maximum length of 1.6 m) is demonstrated using a robot team consisting of three types of robots, even under robot failure and fluctuation in the COM.