四元数矩阵的惯性定理与稳定性

Inertia Theorems and Stability of Quaternion Matrix

本文给出了四元数矩阵惯性的定义,讨论了四元数体上Lyapunov矩阵方程的唯一解,推广了一般惯性定理、Lyapunov稳定性定理、Carlson-Schneider定理、Stein稳定性定理等一些重要的结果到四元数矩阵,同时得出了四元数体上稳定矩阵的一些判别条件.

In this paper, we give the definitions of inertia of quaternion matrix and discuss the unique solution of Lyapunov matrix equation over quaternion field. We extend the general inertia theorem, Lyapunov stability theorem, Carlson-Schneider theorem, Stein stability theorem and some results to quaternion matrices. We obtain some conditions for stable matrix over quaternion.