Stabilization of nonlinear quadratic systems

The authors consider the nonlinear quadratic control system Mdw/dt=Aw+f(w)+g(w, u), where M and A are 3/spl times/3 matrices and, for a fixed m-vector u, f(w) and g(w,u) are quadratic in the 3-vector w=(x, y, z)'. Several theorems and examples that explore the relationship between the quadratic function and the matrices that are involved are presented.