The problem of input-output triangular decoupling and data sensitivity is studied for the case of linear time-invariant systems. Using a static feedback law, the necessary and sufficient conditions for the problem to have a solution are established. The conditions are derived in terms of the variations of the system matrices. The general solution of the controller matrices is also derived. The necessary and sufficient conditions for triangular decoupling and data sensitivity with simultaneous asymptotic stability are established. The structural property of the perturbation-disturbance equivalence is also established.