Existence of linear feedback control for certain types of global stability

Deals with a class of nonlinear control systems of the form x´=Ax+f(x)+Bu where the nonlinear term f(x) is quadratic and has the orthogonality property x^Tf(x)=0 for all x. In the context of Lyapunov´s second method, the existence of a linear feedback control u=Kx is examined. Sufficient conditions are discussed for the system to be controlled to a system with the origin as a global asymptotic stable point or to a system which is point dissipative. A system is point dissipative if there exists a bounded region into which every trajectory eventually enters and remains