Stabilization of Nonlinear Systems using Weak-Control-Lyapunov Functions

This paper proposes a recursive method of constructing weak-control-Lyapunov functions for nonlinear systems. Lyapunov function is one of effective tools to study stability and stabilization in nonlinear system control design. However, a general way of finding Lyapunov functions has not been known yet. Our method is introduced by an explicit topological-geometric assumption for a state space manifold, called a Morse-Smale. The assumption indicates that there exists a sequence of inclusions of the manifold and its singular structures, called a weakLyapunov filtration. From this structure, we can construct a finite number of iterations to define weak-control-Lyapunov functions. As a result, the existence of the weak-control-Lyapunov functions can be specified by the investigation of property of manifolds.