Linear feedback control for a class of nonlinear systems

The authors discuss a class of nonlinear vector systems that admit a Lyapunov function of the form V(x)=(x-α)^Tρ(x -α). Examples of this class include Lorenz´s system, the starting point for the modern study of systems with chaotic attractors, and Euler systems arising in the study of rotational motion of rigid and linked systems such as satellites and robots. In the context of Lyapunov´s second method, sufficient conditions that produce either of the following two types of global behavior are discussed: the origin is a global asymptotic stable point or the system is point dissipative. Associated with each set of conditions is a linear algebra problem relating to controllability