Invented global exponential stabilizable rule of some class of nonlinear control systems and its practical application

An invented necessary and sufficient rule, without providing the troublesome so-called "interconnection conditions", for global exponential stabilizability of some class of nonlinear control systems and its interesting practical application are proposed in this paper. The globally exponentially stabilizing composite feedback control is given here such that the chosen design manifold becomes an exact integral manifold and the trajectories of the closed-loop systems, starting from any initial states, are steered along the integral manifold to the origin for a sufficiently small parameter.