Homogeneous eigenvalue analysis of homogeneous systems

Authors:	Nakamura Hisakazu, Nara Institute of Science and Technology, Japan Yamashita Yuh, Hokkaido University, Japan Nishitani Hirokazu, Nara Institute of Science and Technology, Japan
Topic:	2.3 Non-Linear Control Systems
Session:	Nonlinear Stability II
Keywords:	nonlinear control systems, eigenvalue problems, instability, stability analysis

Abstract

This paper focuses on the problem of stability in homogeneous systems with dilation.First, we propose an `homogeneous eigenvalue' for homogeneous systems.Next, we analyze the stability of homogeneous systems using homgeneous eigenvalues, and we show that the use of positive real homogeneous eigenvalues implies instability. Finally, we show the effectiveness of the proposed method through an example.