Numerical Realization of Plane CW Complexes Under a Given `Flow Condition´ in Gradient-like Morse-Smale Controlled Systems

In this paper, we discuss a global stabilization problem for a two-dimensional nonlinear system from the perspective of the ´realization problem of global compact attractors´ in the theory of gradient-like Morse-Smale controlled systems. We give the topological structure of a desired compact attractor using a graphic data of the corresponding normal CW complex. The control system configuration space is the direct-product of the state space and the input space. From the topological intersection theory in the configuration space, we derive a topological obstruction for controlled systems, which called the ´flow condition´. We propose a solving algorithm for this realization problem and discuss some numerical results.