Aim　at　the　fore　and　aft　asymmetry　of　unmanned　surface　vehicle　(USV)　and　the　loss　of　linear　velocity,　a　static　output　feedback　(SOF)　(Formula　presented.)　control　method　is　proposed　by　the　sum　of　squares　(SOS)　based　on　two　types　of　extended　bounded　real　lemmas　(EBRL)　for　heading　regulation　to　guarantee　the　robustness　and　improve　the　rapidity.　First,　an　asymmetric　nonlinear　heading　error　model　with　hydrodynamic　parameters　is　established　by　the　consideration　of　lack　of　linear　velocity.　Second,　SOF　controller　with　(Formula　presented.)　performance　is　presented　for　the　asymmetric　nonlinear　USV　model,　and　it＇s　SOS　conditions　to　solve　controller　parameters　is　deduced　from　EBRL　by　homogeneous　Lyapunov　function　(HERBL)　to　maintain　the　system　robustness.　Further,　the　solution　of　SOF　(Formula　presented.)　controller　relies　on　the　state　feedback　gain　matrix,　EBRL　is　deduced　by　quadratic　Lyapunov　function　(QEBRL)　to　obtain　the　SOS　conditions　without　the　addition　of　an　extended　matrix　to　cut　computing　cost　for　the　solution　of　the　state　feedback　gain　matrix.　Finally,　the　heading　control　simulations　for　USV　indicate　that,　QEBRL　method　takes　less　time　for　SOS　conditions　to　solve　the　state　feedback　gain　matrix,　and　SOF　(Formula　presented.)　system　of　HERBL　has　a　superior　performance　on　the　transient　response　and　the　robustness.　©　2022　John　Wiley　&　Sons　Ltd.