Influence of anti-diagonals on the asymptotic stability for linear differential systems (Q1027753)

This paper studies sufficient conditions for the asymptotic stability of the linear differential system \(x' = B(t) x\) with \(B(t)\) being a \(2\times 2\) matrix. The matrix \(B(t)\) can be divided into the sum of a diagonal matrix \(D(t)\) and an anti-diagonal matrix \(A(t)\). The author tries to clarify the effect of the anti-diagonal part \(A(t)x\) to the asymptotic stability of the system \(x' = B(t) x\).