Abstract
The paper deals with the global asymptotic stabilization problem for time-invariant general nonlinear state equations from the viewpoint of the topological classification of state feedback controlled systems. A notion of “Boundary tangency manifolds of the state equation” can be derived from the generalized Poincaré-Hopf index formula by C.C. Pugh and C. McCord. We discuss the relation between the boundary tangency manifolds of the state equation and the index formula on the input manifold which is a natural geometrical object for the differentiable state feedback control law. We also introduce terms of the dissipative boundary and the neutral boundary of the state equation and discuss the elementary results for the global asymptotic stabilization problem.
