Continuous feedback stabilization of nonlinear control systems by composition operators

The ability to asymptotically stabilize control systems through the use of continuous feedbacks is an important topic theory and applications. In this paper, we provide a complete characterization feedback stabilizability using new approach that does not involve Lyapunov functions. To do so, first develop slight generalization stabilization composition operators characterize in expanded setting. Employing obtained characterizations more general context, establish relationships between stabiliza|bility conventional sense generalized operator sense. This connection allows us show system equivalent stability associated formed from local section vector field inducing system. That is, reduce question . Moreover, universal formula describing all possible stabilizing for given