Conditions are investigated for systems of the form Mx' N+Ax + f(x), where y is quadratic, which yield 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 extensions to more general classes of systems.