linear feedback control of nonlinear systems with a dominating conservative quadratic term

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.