Two controller design methods,  direct method and indirect method, are used to design antiwindup controller for the multipropeller aerostat with asymmetric actuator constraints. A linear transformation is applied to transfer the asymmetric constraint into a symmetric one. As a result, the generalized sector condition is used to deal with the saturation nonlinearity. By using a quadratic Lyapunov function, linear matrix inequality (LMI) based synthesis condition is presented to address the problem of L2 performance analysis of the saturation constraint closedloop system. The indirect method and the direct method are applied to design controller. The solution of the controller is transformed to a convex optimization expressed in a LMI form and solved by YALMIP toolbox. Finally, simulation results of the direct method and the indirect method show their effectiveness.