For　the　nonlinear　parameter-varying　(NPV)　model　of　unmanned　surface　vehicle　with　the　consideration　of　the　velocities　on　yaw　and　surge　as　well　as　wave　disturbances,　a　robust　(Formula　presented.)　control　method　is　proposed　based　on　extended　homogeneous　polynomial　Lyapunov　function　(EHPLF)　to　regulate　heading　for　the　superior　performance　on　the　rapidity,　accuracy,　and　robustness.　First,　a　NPV　model　of　heading　error　is　established　to　design　a　general　form　of　a　state　feedback　controller　with　a　robust　(Formula　presented.)　performance.　Second,　a　Lyapunov　matrix　with　full　states　and　varying　parameter　is　constructed　to　derive　the　robust　(Formula　presented.)　global　exponential　stability　conditions　by　Euler＇s　homogeneity　relation　for　the　NPV　system,　known　as　the　EHPLF　stability　conditions.　Third,　since　the　EHPLF　stability　conditions　consist　of　a　set　of　nonlinear　coupled　inequalities　that　cannot　be　directly　solved　by　sum　of　squares　(SOS)　toolboxes,　they　are　decoupled　with　matrix　transformations　to　obtain　the　EHPLF-SOS　stability　conditions,　which　is　solved　for　the　parameters　of　the　state　feedback　controller.　Finally,　the　simulation　results　indicate　that　EHPLF　method　exhibits　a　superior　performance　on　dynamic,　steady-state,　and　robustness.　©　2023　John　Wiley　&　Sons,　Ltd.