Conditions are investigated for systems of the form Mx′=N+Ax+f(x), where f is quadratic,
which lield a point dissipative system. Application of the conditions are made to the problem of
existence of linear feedback controls u=Kx for systems of the form
Mx′=N+Ax+f(x)+Bu
which force the system to be point dissipative. The basic results have eztensions to more general
classes of systems.