Title :
Asymptotic Stability Analysis for Homogeneous Systems Using Homogeneous Eigenvalues
Author :
Nakamura, Hisakazu ; Yamashita, Yuh ; Nishitani, Hirokazu
Author_Institution :
Graduate Sch. of Inf. Sci., Nara Inst. of Sci. & Technol., Takayama
Abstract :
Homogeneous eigenvalue analysis is a useful tool for analysis of homogeneous systems. We obtained necessary conditions for asymptotic stability in our previous paper. However, any sufficient conditions are not obtained. In this paper, we introduce Euler sphere, and analyze the properties of solutions of homogeneous systems using dilations of Euler sphere. Moreover, we show the equivalence between a trajectory of a projection of a solution and a trajectory of a solution of a projection system. Then, we prove sufficient conditions for asymptotic stability of homogeneous systems. Finally, we demonstrate the effectiveness of the proposed method for a system which has an uncontrollable linear approximation
Keywords :
asymptotic stability; eigenvalues and eigenfunctions; Euler sphere dilation; asymptotic stability analysis; homogeneous system eigenvalue analysis; projection system trajectory; uncontrollable linear approximation; Asymptotic stability; Control systems; Eigenvalues and eigenfunctions; Equations; Linear approximation; Lyapunov method; Stability analysis; Sufficient conditions; USA Councils; Vectors;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.377542
