This paper considers the design of anti-windup compensators with simple, transparent structures for multivariable constrained input systems. The main results in the paper show how, for multivariable plants with a particular structure, a multivariable anti-windup compensator can be constructed from several “single-loop” anti-windup compensators. Simple conditions, which can be interpreted as a linear program, are then derived which ensure that this concatenated compensator indeed guarantees stability of the multivariable system. The advantages of the resulting compensator is that it is easier to tune, and more transparent for implementation, than an unstructured multivariable compensator. Results from a nonlinear quadrotor simulation show the effectiveness of the proposed method.