Global asymptotic stabilization by using the control Lyapunov function

Authors:	Tsuzuki Takayuki, Hokkaido University, Japan Yamashita Yuh, Hokkaido University, Japan Enomoto Ryuji, Toba National College of Maritime Technology, Japan
Topic:	2.3 Non-Linear Control Systems
Session:	Nonlinear Stability and Structural Analysis
Keywords:	Lyapunov function; Stabilization; Global stability; Singular points; Discontinuous control

Abstract

It is known that if state spaces of control systems are not contractible, the systems are not globally asymptotically stabilizable by using $C^1$ feedback laws. We set multiple singular points of a flow to solve the topological obstruction. Given Morse functions satisfying conditions of the control Lyapunov function except for the singular points, this paper propose a globally asymptotically stabilizing feedback laws of systems on manifolds.