On the nearest stable $ 2\times 2 $ matrix, dedicated to Prof. Sze-Bi Hsu in appreciation of his inspiring ideas
Yueh‐Cheng Kuo, Huan-Chang Cheng, Jhih-You Syu, Shih-Feng Shieh · Discrete and Continuous Dynamical Systems - B · 2020
In this paper, we study the continuous-time nearest stable matrix problem: given a $ 2\times 2 $ real matrix $ A $, minimize the Frobenius norm of $ A-X $, where $ X $ is a stable matrix. We provide an explicit formula for the global minimizer $ X_* $. The uniqueness of the minimizer is also studied.