On characteristic families of dissipative boundaries for two-dimensional gradient-like Morse-Smale controlled systems

The method of gradient-like Morse-Smale controlled (GLMSC) systems is a systematic approach to solve global asymptotic stabilization problems for finite and nonlinear state equations. A GLMSC system is a closed loop system equipped with the structure of a gradient-like Morse-Smale flow. In general, the system has finitely many hyperbolic singular points of the vector field. Its global compact attractor can be represented as a normal CW-complex (CWC). For a fixed combination of hyperbolic singular points, there appear a vast number of corresponding CWCs with different structures. In this paper, we investigate an identification technique for these CWCs with the same singular point data and propose a notion of ´characteristic families of dissipative boundaries´ for distinguishing a given CWC from others.