Tsuzuki, Takayuki (Hokkaido Univ.), Yamashita, Yuh (Hokkaido Univ.)

Global Asymptotic Stabilization of Multi-Input Affine Systems by Using Control Lyapunov-Morse Function

Scheduled for presentation during the Regular Session "Switched Systems I" (MoA05), Monday, July 24, 2006, 12:05−12:30, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

The purpose of this paper is to solve the global asymptotic stabilization problem of multi-input affine systems on general manifolds. It is known that if state spaces of control systems are not contractible, the systems are not globally asymptotically stabilizable via differentiable feedback law, because gradient-like flows on the noncontractible manifolds demand multiple equilibrium points. In this paper, we define a control Lyapunov-Morse function (CLMF) having multiple critical points. The CLMF is an extended control Lyapunov function to have multiple critical points. We derive a discontinuous feedback law from the CLMF. Moreover, a condition of global asymptotic stability of the controlled system with the feedback law is also obtained.