Global Asymptotic Stabilization for a Nonlinear System on a Manifold via a Dynamic Compensator

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  • TSUZUKI Takayuki
    Interdisciplinary Faculty of Science and Engineering, Shimane University
  • YAMASHITA Yuh
    Graduate School of Information Science and Technology, Hokkaido University

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  • 動的補償器による多様体上の非線形制御系の大域漸近安定化
  • ドウテキ ホショウキ ニ ヨル タヨウタイ ジョウ ノ ヒセンケイ セイギョケイ ノ タイイキゼンキン アンテイカ

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Abstract

The purpose of this paper is to solve a global asymptotic stabilization problem for a nonlinear control system on a manifold with a complete metric. As well known, a system on a noncontractible manifold is not globally asymptotically stabilizable via a continuous feedback law. This problem results from the existence of multiple singular points of such a controlled system. It is shown that if all singular points can be assigned to a subspace of the extended state space using a dynamic compensator and a continuous feedback except for at most one jump, then the augmented system becomes globally asymptotically stable. Moreover, a method for stabilization is developed using a dynamic compensator and a global control Lyapunov function for an input-affine system. Finally, we propose a method for constructing the control Lyapunov function for a system such that the dimension of the coefficient matrix of the input is equal to the dimension of the state.

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