For the BTT attitude tracking control problem of hypersonic vehicle,a state-error-space implementation expression of nonlinear H∞ attitude tracking control for above nonlinear coupling system is given firstly.Then basing on γ-energy-dissipation and L2 gain performance criterion in nonlinear system theory,the smooth differentiable stored-energy function is designed,which subject to the Hamilton-Jacobi-Isaacs inequality.Following some assumptions,a local state-space solution of nonlinear H∞ attitude-tracking control problem for nonlinear coupling hypersonic vehicle system is obtained,by using Riccati differential equation of linear following system in local state-space.The local state-space is the neighborhood around the command state error space.Above approach avoids complicated solving process of Hamilton-Jacobi-Isaacs inequality,thus it’s a good reference for engineering.