This　paper　addresses　the　nonlinear　\mathrm{H}-{\infty}　fault　tolerant　control　(FTC)　problem　for　a　quadrotor　unmanned　aerial　vehicle　(UAV),　with　convex　polytopic　faults　in　motors.　Based　on　Rodrigues　parameter　description,　the　attitude　dynamic　of　the　quadrotor　is　modeled　in　a　state　dependent　linear-like　form.　By　using　Lyapunov　stability　and　positive　polynomial　theories,　the　sufficient　conditions　for　stabilization　with　and　without　\mathrm{H}-{\infty}　performance　of　the　UAV　system　are　formulated　in　terms　of　state-dependent　linear　matrix　inequalities　which　can　be　verified　by　sostools　in　MATLAB.　Numerical　simulation　results　show　the　effectiveness　in　accommodating　loss　of　motor　effectiveness.　©　2018　IEEE.